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About Google Book Search Google's mission is to organize the world's information and to make it universally accessible and useful. Google Book Search helps readers discover the world's books while helping authors and publishers reach new audiences. You can search through the full text of this book on the web at jhttp : //books . qooqle . com/ [gitized by Google Digitized by VjOOQ IC Digitized by VjOOQ IC Digitized by VjOOQ IC Digitized by VjOOQLC ■ELECTRO-DYNAMIC MACHINERY- FOR CONTINUOUS CURRENTS BY EDWIN J. HOUSTON, Ph. D. (Princeton) n * AND A. E. KENNELLY, Sc. D. NEW YORK THE W. J. JOHNSTON COMPANY 253 Broadway 1896 Digitized by VjOOQ IC . I Copyright, 1896, by THE W. J. JOHNSTON COMPANY. Digitized by VjOOQ IC PREFACE. Although several excellent treatises on machinery employed in electro-dynamics already exist, yet the authors believe that there remains a demand for a work on electro-dynamic ma- chinery based upon a treatment differing essentially from any that has perhaps yet appeared. Nearly all preceding treatises are essentially symbolic in their mathematical treatment of the quantities which are in^olyecL even although such treat- ment is associated with much practical information. It has been the object of the authors in this work to employ only the simplest mathematical treatment, and to base this treatment, as far as possible, on actual observations, taken from practice, and illustrated by arithmetical examples. By thus bringing the reader into intimate association with the nature of the quantities involved, it is believed that a more thorough appre- ciation and grasp of the subject can be obtained than would be practicable where a symbolic treatment from a purely algebraic point of view is employed. In accordance with these principles, the authors have in- serted, wherever practicable, arithmetical examples, illustrat- ing formulas as they arise. The fundamental principles involved in the construction and use of dynamos and motors have been considered, rather than the details of construction and winding. The notation adopted throughout the book is that recom- mended by the Committee on Notation of the Chamber of Delegates at the Chicago International Electric Congress of 1893. iii Digitized by VjOOQ IC IV PREFACE. The magnetic units of the C. G. S. system, as provisionally adopted by the American Institute of Electrical Engineers, are employed throughout the book. The advantages which are believed to accrue to the concep- tion of a working analogy between the magnetic and voltaic circuits, are especially developed, for which purpose the con- ception of reluctivity and reluctance are fully availed of. Digitized by VjOCK CONTENTS. CHAPTER I. GENERAL PRINCIPLES OF DYNAMOS. Definition of Electro-Dynamic Machinery. General Laws of the Genera- tion of E. M. F. in Dynamos. Electric Capability. Output. Intake. Commercial Efficiency. Electrical Efficiency. Maximum Output. Maximum Efficiency. Relation between Output and Efficiency, I CHAPTER II. STRUCTURAL ELEMENTS OF DYNAMO-ELECTRIC MACHINES. Armatures. Field Magnets. Magnetic Flux. Commutator Brushes. Constant- Potential Machines. Constant-Current Machines. Magneto- Electric Machines. Separately-Excited Machines. Self-Excited Machines. Series- Wound Machines. Shunt- Wound ' Machines. Compound- Wound Machines. Bipolar Machines. Multipolar Ma- chines. Quadripolar, Sextipolar, Octopolar and Decipolar Machines. Number of Poles Required for Continuous and Alternating-Current Machines. Consequent Poles. Ring Armatures. Drum Armatures. Disc Armatures. Pole Armatures. Smooth-Core Armatures. Toothed- Core Armatures. Inductor Dynamos. Diphascrs. Triphasers. Single Field-Coil Multipolar Machines. Commutatorless Continuous- Current Machines, 9 CHAPTER III. MAGNETIC FLUX. Working Theory Outlined. Magnetic Fields. Direction, Intensity, Dis- tribution. Uniformity, Convergence, Divergence. Flux Density. Tubes of Force. Lines of Magnetic Force. The Gauss. Properties of Magnetic Flux. M. M. F. Ampere-Turn. The Gilbert. Flux Paths, .29 CHAPTER IV. NON-FERRIC MAGNETIC CIRCUITS. Reluctance. The Oersted. Ohm's Law Applied to Magnetic Circuits. Ferric, Non-Ferric, and Aero-Ferric Circuits. Magnetizing Force. Magnetic Potential. Laws of Non-Ferric Circuits, . . .48 CHAPTER V. FERRIC MAGNETIC CIRCUIT. Residual Magnetism. Permeability. Theory of Magnetization in Iron. Prime M. M. F. Structural M. M. F. Counter M. M. F. Reluc- tivity. Laws of Reluctivity. . . .55 Digitized by VjOOQ IC Vin CONTENTS. CHAPTER VI. AERO-FERRIC MAGNETIC CIRCUITS. Magnetic Stresses. Laws of Magnetic Attraction. Leakage, . « . 6£ CHAPTER VII. LAWS OF ELECTRO-DYNAMIC INDUCTION. Fleming's Hand Rule. Cutting and Enclosure of Magnetic Flux, , . 74 CHAPTER VIII. ELECTRO-DYNAMIC INDUCTION IN DYNAMO ARMATURES. Curves of E. M. F. Generated in Armature Windings. Idle- Wire, . 90- CHAPTER IX. ELECTROMOTIVE FORCE INDUCED BY MAGNETO GENERATORS, IO3. CHAPTER X. POLE ARMATURES, IIO* CHAPTER XI. GRAMME-RING ARMATURES. E. M. Fs. Induced in. Effect of Magnetic Dissymmetry. Commuta- tor-Brushes. Effect of Dissymmetry in Winding. Best Cross- Section of Armature, . . . . . . . . .117 CHAPTER XII. CALCULATION OF THE WINDINGS OF A GRAMME-RING DYNAMO, I2& CHAPTER XIII. MULTIPOLAR GRAMME-RING DYNAMOS. Belt-Driven versus Direct-Driven Generators. Reasons for Employing Multipolar Field Magnets. Multipolar Armature Connections. Effect of Dissymmetry in Magnetic Circuits of Multipolar Generators. Com- putations for Multipolar Gramme-Ring Generator, . . . .I3S CHAPTER XIV. DRUM ARMATURES. Smooth-Core and Toothed-Core Armatures. Armature Windings. Lap Windings. Wave Windings, 152 CHAPTER XV. ARMATURE JOURNAL BEARINGS. Frictional Losses of Energy in Dynamos. Sight-Feed Oilers and Self- Oiling Bearings, 159 Digitized by VjOOQ LC CONTENTS. ix CHAPTER XVI. EDDY CURRENTS. Methods of Lamination of Core. Transposition of Conductors, . . 164 CHAPTER XVII. MAGNETIC HYSTERESIS. Nature and Laws of Hysteresis. Hysteretic Loss of Energy. Table of Hysteretic Loss. Hysteretic Torque, 172 CHAPTER XVIII. ARMATURE REACTION AND SPARKING AT COMMUTATORS. Diameter of Commutation. E. M. F. of Self-Induction. Inductance of Coils. Cross- Magnetization. Back-Magnetization. Leading and Following Polar Edges. Lead of Brushes. Distortion of Field. Con- ditions Favoring Sparking at Commutator. Conditions Favoring Sparkless Commutation. Methods Adopted for Preventing Sparking, 179 CHAPTER XIX. HEATING OF DYNAMOS. Losses of Energy in Magnetizing, Eddies, Hysteresis and Friction. Safe Temperature of Armatures, 199 CHAPTER XX. REGULATION OP DYNAMOS. Series-Wound, Shunt-Wound and Compound-Wound Generators. Over- compounding. Characteristic Curves of Machines. Internal and External Characteristic. Computation of Characteristics. Field Rheostats. Series- Wound Machines and their Regulation. Open-Coil and Closed-Coil Armatures, 206 CHAPTER XXI. COMBINATIONS OF DYNAMOS IN SERIES AND PARALLEL. Generator Units. Series- Wound Machines Coupled in Series. Shunt- Wound Machines Coupled in Parallel. Equalizing Bars. Omnibus Bars, 220 CHAPTER XXII. DISC-ARMATURES AND SINGLE-FIELD COIL MACHINES, 228 CHAPTER XXIII. COMMUTATORLESS CONTINUOUS-CURRENT GENERATORS. Disc and Cylinder Machines, 234 Digitized by VjOOQ IC X CONTENTS. CHAPTER XXIV. ELECTRO-DYNAMIC FORCE. Fleming's Hand-Rule. Ideal Electro-dynamic Motor, . . . .241 CHAPTER XXV. MOTOR TORQUE. Torque of Single Active Turn. Torque of Armature- Windings. Torque of Multipolar Armatures. Dynamo- Power, 251 CHAPTER XXVI. EFFICIENCY OF MOTORS. Commercial Efficiency in Generators and Motors Compared. Slow-Speed versus High-Speed Motors. Torque-per-pound of Weight, . . 268 CHAPTER XXVII. REGULATION OF MOTORS. Control of Speed and Torque under Various Conditions. Control of Series- Wound Motors, 280 CHAPTER XXVIII. STARTING AND REVERSING OF MOTORS. Starting Rheostats. Starting Coils. Automatic Switches. Direction of Rotation in Motors, . 297 CHAPTER XXIX. METER-MOTORS. Conditions under which Motors may act as Meters, 309 CHAPTER XXX. MOTOR DYNAMOS. Construction and Operation of Motor-Dynamos, • • • o . 3 X & Digitized by VjOOQ LC ELECTRO-DYNAMIC MACHINERY FOR CONTINUOUS CURRENTS. CHAPTER I. GENERAL PRINCIPLES OF DYNAMOS. I. By electro-dynamic machinery is meant any apparatus designed for the production, transference, utilization or measurement of energy through the medium of electricity. Electro-dynamic machinery may, therefore, be classified under the following heads : (i.) Generators, or apparatus for converting mechanical energy into electrical energy. (2.) Transmission circuits, or apparatus designed to receive, modify and transfer the electric energy from the generators to the receptive devices. (3.) Devices for the reception and conversion of electric energy into some other desired form of energy. (4.) Devices for the measurement of electric energy. Under generating apparatus are included all forms of con- tinuous or alternating-current dynamos. Under transmission circuits are included not only conduct- ing lines or circuits in their various forms, but also the means whereby the electric pressure may be varied in transit between the generating and the receptive devices. This would, therefore, include not only the circuit conductors proper, but also various types of transformers, either station- ary or rotary. Under receptive devices are included any devices for con- verting electrical energy into mechanical energy. Strictly speaking, however, it is but fair to give to the term mechanical energy a wide interpretation, such for example, as would per- Digitized by VjOOQ LC 2 ELECTRO-DYNAMIC MACHINERY. mit the introduction of any device for translating electric energy into telephonic or telegraphic vibrations. Under devices for the measurement of electric energy would be included all electric measuring and testing apparatus. In this volume the principles underlying the construction and use of the apparatus employed with continuous-current machinery will be considered, rather than the technique in- volved in their application. 2. A consideration of the foregoing classification will show that in all cases of the application of electro-dynamic machin- ery, mechanical energy is transformed, by various devices, into electric energy, and utilized by various electro-receptive devices connected with the generators by means of conducting lines. The electro-technical problem, involved in the practi- cal application of electro-dynamic machinery, is, therefore, that of economically generating a current and transferring it to the point of utilization with as little loss in transit as possible. The engineering problem is the solution of the electro-technical problem with the least expense. 3. A dynamo-electric generator is a machine in which con- ductors are caused to cut magnetic flux-paths, under conditions in which an expenditure of energy is required to maintain the electric current. Under these conditions, electromotive forces are generated in the conductors. Since the object of the electromotive force generated in the armature js the production of a current, it is evident that, in order to obtain a powerful current strength, either the electro- motive force of the generator must be great, or the resistance of the circuit small. Electromotive sources must be regarded as primarily producing, not electric currents, but electromotive forces. Other things being equal, that type of dynamo will be the best electrically, which produces, under given conditions of resistance, speed, etc., the highest electromotive force (generally contracted E. M. F.). In designing a dynamo, therefore, the electromo- tive force of which is fixed by the character of the work it is required to perform, the problem resolves itself into obtaining a machine which will satisfactorily perform its work at a given Digitized by VjOOQ IC GENERAL PRINCIPLES OF DYNAMOS. 3 efficiency, and without overheating, with, however, the maxi- mum economy of construction and operation. In other words, that dynamo will be the best, electrically, which for a given weight, resistance and friction, produces the greatest electro- motive force. 4. There are various ways in which the electromotive force of a dynamo may be increased; viz., (1.) By increasing the speed of revolution. (2.) By increasing the magnetic flux through the machine. (3.) By increasing the number of turns on the armature. The increase in the speed of revolution is limited by well- known mechanical considerations. Such increase in speed means that the same wire is brought through the same mag- netic flux more rapidly. To double the electromotive force from this cause, we require to double the rate of rotation, which would, in ordinary cases, carry the speed far beyond the limits of safe commercial practice. Since the E. M. F. produced in any wire is proportional to its rate of cutting magnetic flux, it is evident that in order to double the E. M. F. .in a given wire or conductor, its rate of motion through the flux must be doubled. This can be done, either by doubling the rapidity of rotation of the armature ; or, by doubling the density of the flux through which it cuts, the rate of motion of tfte armature remaining the same. Since the total E. M. F. in any circuit is the sum of the separate E. M. Fs. contained in that circuit, if a number of separate wires, each of which is the seat of an E. M. F., be connected in series, the total E. M. F. will be the sum of the separate E. M. Fs. If, therefore, several loops of wire be moved through a magnetic field, and these loops be con- nected in series, it is evident that, with the same rotational speed and flux density, the E. M. F. generated will be pro- portional to the number of turns. An increase in E. M. F. under any of these heads is limited by the conditions which arise in actual practice. As we have already seen, the speed is limited by mechanical considerations. An increase in the magnetic flux is limited by the magnetic permeability of the iron — that is, its capability of conducting magnetic flux — and the increase in the number of turns is Digitized by VjOOQ IC 4 ELECTRO-DYNAMIC MACHINERY. limited by the space on the armature which can properly be devoted to the winding. 5. It will be shown subsequently that a definite relation exists between the output of a dynamo, and the relative amounts of iron and copper it contains — that is to say, the type of machine being determined upon, given dimensions and weight should produce, at Q given speed, a certain output. The conditions under which these relations exist will form the subject of future consideration. 6. Generally speaking, in the case of every machine, there exists a constant relation between its electromotive force and resistance, which may be expressed by the ratio, — , where £ f r is the E. M. F. of the machine at its brushes, in volts, and r, the resistance of the machine; i. e., its internal resistance, in ohms. In any given machine, the above ratio is nearly con- stant, no matter what the winding of the machine may be; /. e. f no matter what the size of the wire employed.* This ratio may be taken as representing, in watts, the electric activity of the machine on short circuit, and may be con- veniently designated the electric capability of the machine. For example, in a 200, KW (200,000 watts) machine; i. e., a dynamo, whose output is 200 KW (about 267 horse power), the value of the electric capability would be about 10,000 KW, so that, since — = 10,000,000, if its E. M. F. were 155 volts, its resistance would be 0.0024 ohm; whereas, if its E. M. F. were 100 volts, its resistance would be approximately 0.001 ohm. 7. HithertQ we have considered the energy absorbed by the dynamo, independently of its external circuit — that is, we have considered only the electric capability of the machine. When the dynamo is connected with an external circuit, two extreme cases may arise ; viz., * This ratio would be constant if the ratio of insulation thickness to diameter of wire remained constant through all sizes of wire. Digitized by VjOOQ LC GENERAL PRINCIPLES OF DYNAMOS. 5 (i.) When the resistance of the external circuit is very small, so that the machine is practically short circuited. Here all the electric energy is liberated within the machine. (2.) When the external resistance is so high that the resist- ance of the machine is negligible in comparison. Here practi- cally all the energy in the circuit appears outside the machine. The total amount of work, however, performed by the machine, under these circumstances, would be indefinitely small, since the current strength would be indefinitely small. Between these two extreme cases, an infinite number of intermediate cases may arise. 8. By the output of a dynamo is meant the electric activity of the machine in watts, as measured at its terminals; or, in other words, the output is all the available electric energy. Thus, if the dynamo yields a steady current strength of 500 amperes at a steady pressure or E. M. F., measured at its termi- nals, of no volts, its output will be no X 500 = 55,000 watts, or 55 kilowatts. The intake of a dynamo is the mechanical activity it absorbs, measured in watts. Thus, if the dynamo last considered were driven by a belt, which ran at a speed of 1,500 feet-per-minute, or 25 feet-per-second, and the tight side of the belt exerted a stress or pull of 2,500 pounds weight, while the slack side exerted a pull of 710 pounds weight, the effective force, or that exerted in driving the machine, would be 1,790 pounds weight. This force, moving through a distance of 25 feet per second, would develop an activity represented by 1,790 X 25=44,750 foot-pounds per second; and one foot- pound per second is usually taken as 1.355 watts, so that the intake of the machine is 60,630 watts, or 60.63 KW. By the commercial efficiency of a dynamo is meant the ratio of its output to its intake. In the case just considered, the com- mercial efficiency of the machine would be , y - = 0.9072. By the electric efficiency of a dynamo is meant the output, divided by the total electric activity in the armature cir- cuit. Thus, if the dynamo just considered had a total electric energy in its circuit of 57 KW, of which 2 KW were expended in the. machine, its electric efficiency would be — = 0.965. Digitized by VjOOQ LC 6 ELECTRO-DYNAMIC MACHINERY. 9. The output of a machine would be greatest when the external resistance is equal to the resistance of the machine. In this case, the output would be just one-quarter the electric capability, and the electric efficiency would be 0.5. Thus, the resistance of the dynamo considered in the preceding para- graph would be, say, 0.008 ohm, and the electric capability of no' the machine ~ = 1,512,500 watts, or 1,512.5 KW. If the O.OOo external resistance were equal to the internal resistance — namely, 0.008 ohm, the total activity in the circuit would be 756.25 KW; the output would be 378.12 KW, and the electric efficiency 0.5. That is to say, in order to obtain a maximum output from a dynamo machine, the circumstances must be such that half the electric energy is developed in the machine, and half in the external circuit; or, in other words, the electric efficiency can be only 0.5. In practice, however, it would be impossible to operate a machine of any size under these circumstances, since the amount of energy dissipated in the machine would be so great that the consequent heating effects might destroy it. 10. We have seen that whenever the resistance in the external circuit is indefinitely great, as compared with that of the machine, the electric efficiency of the machine will be 1.0 or 100 per cent. It is evident, therefore, that in order to increase the electric efficiency of a dynamo, it is necessary that the resistance. of the external circuit be made great, com- pared with the internal resistance of the machine. For ex- ample, if the external resistance be made nine times greater than that of the internal circuit, then the electric efficiency will be — - — = 0.0; and, similarly, if the external resistance be nineteen times that of the internal resistance, the electric efficiency would be raised to — -?— = 0.95. Generally speak- ing, therefore, a high electric efficiency requires that the internal resistance of the machine be small as compared with the external resistance, and, also, that the amount of power Digitized by VjOOQ IC GENERAL PRINCIPLES OF DYNAMOS. 7 expended in local circuits, as in magnetizing the field magnets of the dynamo, be relatively small. 11. Care must be taken not to confound the electric efficiency of a machine with its electric output. The electric output of a machine would reach a maximum when the electric efficiency was 0.5 or 50 per cent, and the output would be zero when the electric efficiency reached 1.0. The electric efficiency of the largest dynamos is very high, about 0.985. Indeed, the electric efficiency of large machines must necessarily be made high, since, otherwise, the libera- tion of energy within them would result in dangerous over- heating. The commercial efficiency of a dynamo is always less than its electric efficiency, since all mechanical and magnetic frictions, such as air resistance, journal-bearing friction, hysteresis and eddy currents come into account among the losses. The commercial efficiency also depends upon the type of machine, whether it be belt-driven, or directly mounted on the engine shaft, since the mechanical frictions to be overcome differ markedly in these two cases. The commercial efficiency will also vary with the character of the iron employed in its field magnets and armature, and with the care exercised in securing its proper lamination. In large machines, of say 500 KW capacity, the commercial efficiency may be as high as 0.95. In very small machines, of say 0.5 KW, the highest commercial efficiency may be only 0.6. 12. Although in the United States it is the practice among constructors generally, to calculate, express and compare lengths and surface areas in inches and square inches, when referring to dynamo machinery, and although it might seem therefore more suitable to adopt inches and square inches as units of length and surface throughout this book; yet the fact that the entire international system of electro-magnetic meas- urement is based on the centimetre, renders the centimetre and square centimetre the natural units of dimensions in electro- magnetism. The authors have therefore preferred to base Digitized by VjOOQ LC 8 ELECTRO-DYNAMIC MACHINERY. the formulae and reasoning in this volume on the French fundamental units, in order to simplify the treatment, wett knowing that once the elementary principles have been grasped, the transition to English measurements is easily effected by the student. The following data will, therefore, be useful : i inch = 2.54 cms. I cm. = 0.3937 inch. . 1 foot = 30.48 cms. 1 cm. = 0/03281 foot. 1 sq. inch = 6.4515 sq. cms. 1 sq. cm. = 0.155 sq. in. 1 cubic inch = 16.387 c. c. x c. c. = 0.06102 c. in. Digitized by VjOOQ IC CHAPTER II. STRUCTURAL ELEMENTS OF DYNAMO-ELECTRIC MACHINES. 13. Dynamo-electric machines, as ordinarily constructed, consist essentially of the following parts; namely, (1.) Of the part called the armature, in which the E. M. F. is generated. The armature is generally a rotating part, although in some machines the armature is fixed, and either the field magnets, or the magnetic field, revolve. (2.) Of the part in which the magnetic field is generated. This part is called the field magnet and provides a magnetic flux through which the conductors of the armature are generally, actually, and always relatively, revolved. (3.) Of the part or parts that are employed for the pur- pose of collecting and rectifying the currents produced by the E. M. F. generated in the armature; /. *., collecting and commuting them, and causing them to flow in one and the same direction in the external circuit. This portion is called the commutator. (4.) Bundles of wire, metallic plates, metallic gauze, or plates of carbon, pressed against the commutator, and con- nected with the circuit in which the energy of the machine is utilized. These are called the brushes. In addition to the above parts, which are directly connected with the electric actions of the machine, there are the neces- sary mechanical parts, such as the bearings, shaft, keys, base, etc., which also require attention. The particular arrangement of the different parts will neces- sarily depend upon the type of machine, as well as on the char- acter of the circuit which the machine is designed to supply. It will, therefore, be advisable to arrange dynamo-electric machines into general classes, before attempting to describe the structure and peculiarities of their various parts. 14. Dynamos may be conveniently divided into the follow- ing classes; viz., Digitized by VjOOQ LC IO ELECTRO-DYNAMIC MACHINERY. (i.) Constant potential machines, or those designed to main- tain at their terminals a practically uniform E. M. F. under all variations of load. To this class belong nearly all dynamos for supplying incan- descent lamps and electric railroads. Fig. i represents a particular machine of the constant- potential type. A, A, is the armature, whose shaft revolves in the self-oiling bearings £, B. C is the commutator, and D y D, are triple sets of brushes pressing their tips or ends upon FIG. I. — CONTINUOUS-CURRENT BIPOLAR CONSTANT-POTENTIAL GENERATOR. the commutator. F, F, are the field magnets, wound with coils of insulated wire. T, T, are the machine terminals, con- nected with the brushes and with the external circuit or. load. The whole machine rests on slides with screw adjustment for tightening the driving belt. Constant-potential generators are made of all sizes, and of various types. (2.) Constant-current machines, or those designed to main- tain an approximately constant current under all variations of load. Digitized by VjOOQ LC STRUCTURAL ELEMENTS. II Constant-current machines are employed almost exclusively for supplying arc lamps in series. Fig. 2 represents a form of constant-current generator. This is an arc-light machine. It has four field magnets but only two poles, P x and I", connected by a bridge of cast iron at B. At R^ is a regulating apparatus for automatically main- taining the constancy of the current strength, by rotating the FIG. 2. — CONTINUOUS CONSTANT-CURRENT BIPOLAR GENERATOR. brushes back or forward over the commutator, under the influ- ence of an electromagnet M. Constant-current machines are made for as many as 200 arc lights; i. *., about 10,000 volts and 9 amperes, or an output up to 90 kilowatts capacity, but such large sizes are exceptional. 15. Constant-potential machines may be subdivided into sub-classes, according to the arrangement for supplying their magnetic flux — namely: (a.) Jtfagneto-electric machines, in which permanent magnets are employed for the fields. The magneto-electric generator was the original type and progenitor of the dynamo, or dynamo-electric generator — but Digitized by VjOOQ LC 12 ELECTRO-DYNAMIC MACHINERY, has almost entirely disappeared. It is, however, still used in telephony, the hand call being a small alternating-current mag- neto generator, driven by power applied at a handle. The magneto-electric generator is also used in firing mining fuses, and in some signaling and electro-therapeutic apparatus. Fig. 3 represents a form of magneto-electric generator. M, is a triple group of permanent magnets, and A, is the armature. (b.) Separately-excited machines, in which the field electro- magnets are excited by electric current from a separate elec- tric source. FIG. 3. — ALTERNATING-CURRENT MAGNETO-ELECTRIC GENERATOR. A particular form of separately excited generator is repre- sented in Fig. 4. Here a generator A, has its field magnets supplied by a small generator B, employed for this sole purpose. It is not necessary, however, that the exciting machine be used exclu- sively for excitation. Thus two generators, each employed in supplying a load, and each supplying the field magnets of the other, would be mutually separately excited. In central stations large continuous-current machines are occasionally, and alternating-current machines are usually, separately excited. (c.) Self -excited machines, or generators whose field magnets are supplied by currents from the armature. Fig. 5 represents a form of self-excited generator. M, M, are the field magnets, P y the pilot lamp; i. e. f a lamp connected across the terminals of the machine, to show that the generator is at work. S, the main circuit switch, R, the rocker-arm carrying the brushes B, B. Digitized by VjOOQ LC STRUCTURAL ELEMENTS. 13 16. Self-excited machines maybe divided into three classes; ^viz., (1.) Series wound. (2.) Shunt wound. (3.) Compound wound. Series-wound machines have their field magnets connected in series with their armatures. The field winding consists of FIG. 4. — ALTERNATING- CURRENT MULTIPOLAR SEPARATELY-EXCITED GENERATOR. stout wire, in comparatively few turns. Arc-light machines are almost always series wound. Fig. 6 represents a particular form of series-wound machine for arc-light circuits. Here the current from the armature passes round the cylindrical mag- nets M 9 M, through the regulating magnet m, and thence to the external circuit. The machine in Fig. 2 is also series wound. Shunt-wound machines have their field magnets connected to the main terminals, that is, placed in shunt with the external circuit. In order to employ only a small fraction of .the total current from the armature for this purpose, the resistance of the field magnets is made many times higher than the resist- Digitized by VjOOQ IC 14 ELECTRO-DYNAMIC MACHINERY. ance of the external circuit. This is accomplished by winding the magnets with many turns of fine wire, carefully insulated. A particular form of shunt-wound machine is represented in Fig. 7. Here the fine wire windings of the four magnets coils are supplied in one series through the connecting wires W> W y W y FIG. 5. — SELF-EXCITED CONTINUOUS-CURRENT GENERATOR. from the main terminals of the machine, one of which is shown at M. In order to regulate the strength of the exciting cur- rent through the magnet circuit, it is usual to insert a hand- regulating resistance box, called the field regulating box, in series with them. (d.) Compound-wound machines. These are machines that are partly shunt wound and partly series wound. It is found that when the load increases on a series-wound generator, it tends to increase the pressure at its terminals ; i.e., to raise its E. M. F. On the other hand, when the load increases on a shunt-wound generator, it tends to diminish the pressure at its terminals; /. e., to lower its E. M. F. In order, therefore, to obtain good automatic regulation of pressure Digitized by VjOOQ LC STRUCTURAL ELEMENTS, 15 from a machine under all loads, these two tendencies* are so directed as to cancel each other ; this is accomplished by employing a winding that is partly shunt and partly series. Fig. 8 represents a particular form of a compound-wound machine. Here there are two spools placed side by side on each mag- net-core, one of fine wire in the shunt circuit, carrying a cur T rent, and exciting the fields, even when no current is supplied externally by the machine, and the other of stout wire making FIG. 6. — SELF-EXCITED SERIES-WOUND CONTINUOUS-CURRENT GENERATOR. comparatively few turns. This is part of the series winding which carries the current to the external circuit. The excita- tion of the magnets from this winding, therefore, depends upon the current delivered by the machine; /. S, in each case, the field coils being so wound and excited a^ to produce consequent poles. FIG. 15. — CONTINUOUS-CURRENT CONSEQUENT-POLE BIPOLAR GENERATOR. 22. Dynamo machines may also be classified according to the shape of the armature, as follows; namely, (a.) Ring armatures. (b. ) Cylinder or drum armatures. (c. ) Disc armatures. (d. ) Radial or pole armatures. (e. ) Smooth-core armatures. (f. ) Toothed-core armatures. Figs. 2 and 11 represent examples of ring armatures. Since Gramme was the first to introduce the ring type of armature, this form is frequently called a Gramme-ring armature. Figs. 1, 5 and 14, show examples of cylinder or drum arma- tures. Disc armatures are very seldom employed in the United States. An example of a disc armature is shown in Fig. 19. An example of a radial or pole armature is seen in Fig. 17. Digitized by VjOOQ LC *4 ELECTRO-DYNAMIC MACHINERY. A smooth-core armature is one on which the wire is wound over the cylindrical iron core, so as to cover the armature sur- face completely; or, if the wire does not cover the surface com- pletely, the space between the wires may either be left vacant or filled with some non-magnetic metal. Such armatures are represented in Figs, i, 2, 5, 15. A toothed-core armature, on the other hand, is one on which FIG. 16. — ALTERNATING-CURRENT SEPARATELY-EXCITED I2-POLE GENERATOR. the wire is so wound in grooves or depressions, on the surface of the laminated iron core, that the finished armature pre- sents an ironclad surface, but with slots containing insulated copper wire. Such an armature is shown in Fig. 18 and also in Figs. 7, 10 and 11. It is frequently called an iron-clad armature. Digitized by VjOOQ IC STRUCTURAL ELEMENTS. *5 23. Dynamos may also be divided, according to the actual or relative movement of armature or field, into the following classes; namely, (a.) Those in which the field is fixed and the armature FIG. 17. — DIAGRAM OF POLE ARMATURE. revolves. This class includes all the machines previously described, except that represented in Fig. 19. (b.) Those in which the armature is fixed and the field revolves. An example of this type of machine is shown in FIG. l8. — A TOOTHED-CORE ARMATURE SHOWING THE STAGES OF WINDING. Fig. 19 A and B, where two sets of field magnets, mounted on a common shaft, revolve together around a fixed disc arma- ture, shown in Fig. 19 B, which is rigidly supported vertically in the space between them. (c.) Those in which the field and armature are both fixed, but the magnetic connection between the two is revolved. These dynamos are usually called inductor dynamos. Digitized by VjOOQ LC 26 ELECTRO-DYNAMIC MACHINERY. 24. Dynamo machines may also be divided, according to the character of the work they are intended to perform, into the following classes; namely, (a.) Arc-light generators, (b. ) Incandescent-light generators. (c. ) Plating generators. (d.) Generators for operating motors. •"SB J m FIG. I9A. — ALTERNATING-CURRENT DOUBLE I2-POLE GENERATOR WITH FIXED ARMATURE AND REVOLVING FIELD FRAMES. (e. ) Telegraphic generators. (f. ) Therapeutic generators. (g.) Welding generators. 25. Alternating-current generators may be divided, accord- ing to the number of separate alternating currents furnished by the machine, into the following classes; namely, (a.) Uniphase alternators, or those that deliver a single alter- nating current. To this class of machines belong all the ordinary alternators employed for electric lighting purposes. (b.) Multiphase alternators, or those that deliver two or more alternating currents which are not in step. Digitized by VjOOQ IC STRUCTURAL ELEMENTS. 27 Some multiphase alternators can supply both single-phase and multiphase currents to different circuits. Multiphase machines may be further subdivided into the following classes; namely, (1.) Diphase machines, or those delivering two separate alter- nating currents. These two currents are, in almost all cases, mm FIG. I9B. — DISC ARMATURE. quarter-phase currents, that is to say, they are separated by a quarter of a complete cycle. Although it is possible to employ any other difference of phase between two currents, yet the quarter-phase is in present practice nearly always employed. Fig. 9 represents a diphase generator, or diphaser. (2.) Triphase machines, or triphasers, are generators deliver- ing three separate alternating currents. These three currents are, in all cases, separated by one third of a complete cycle. Uniphase machines are sometimes called single-phase machines, and diphase machines are sometimes called two-phase machines or tivo-phasers, while triphase machines are sometimes called three-phase machines or three-phasers. The terminology above employed, however, is to be preferred. 26. In addition to the above classification there are the fol- lowing outstanding types : Digitized by VjOOQ IC 28 ELECTRO-DYNAMIC MACHINERY. (a.) Single-field-coil multipolar machines, or machines in -which multipolar magnets are operated by a single exciting field coil. (b.) Commutatorless continuous-current machines, or so-called unipolar machines, in which the E. M. Fs. generated in the arma- ture, being obtained by the continuous cutting of flux in a uniform field, have always the same direction in the circuit, and do not, therefore, need commutation. The term unipolar is both inaccurate and misleading, as a single magnetic pole does not exist. Digitized by VjOOQ IC CHAPTER III. MAGNETIC FLUX. 27. A magnet is invariably accompanied by an activity in the space or region surrounding it. Every magnet produces a magnetic field or flux, which not only passes through the sub- stance of the magnet itself, but also pervades the space sur- rounding it. In other words, the property ordinarily called magnetism is in reality a peculiar activity in the surrounding -ether, known technically d&hnagnt tic flux, ' By a simple convention magnetic flux is regarded as passing out of the north-seeking pole of a magnet, traversing the space Surrounding the magnet, and finally re-entering the magnet at its south-seeking pole. Magnetic flux, or magnetism, is cir- cuital; that is, the flux is active along closed, re-entrant curves. 28. Although we are ignorant of the true nature of magnetic flux, yet,, perhaps, the most satisfactory working conception we can form concerning it, is that of the ether in translatory motion ; in other words, in a magnet, the ether is actually streaming out from the north-seeking pole and re-entering at the south-seeking pole. Since the ether is assumed to possess the properties of a perfect fluid ; 1. e. 9 to be incompressible, readily movable, and almost Jnfinitesimally divisible, it is evident that if a hollow tube, or bundle of hollow tubes, of the same aggregate dimen- sions as a magnet, be conceived to be provided internally with a force pump in each tube, and that such tube be placed in free ether, then, on the action of the force pumps, a streaming would occur, whereby the ether would escape from one end of each of the tubes, traverse the surrounding space, and re-enter at the other ends of the tubes. Moreover, if the stream lines, through which the ether particles would move under such ideal circumstances, were mapped out, they would be found to coin- Digitized by VjOOQ IC 3<> ELECTRO-DYNAMIC MACHINERY. cide with the observed paths which the magnetic stream lines take in the case of a magnet. Similar stream lines could be actually observed in the case of a hollow tube provided internally with a pump, and filled with and surrounded by water ; only, in this case, on account of the friction of the liquid particles, both in the tube and between themselves, work would require to be done and energy expended in maintaining the motion, and, unless such energy FIGS. 20 AND 20A. — DIAGRAMS REPRESENTING A TUBE, IMMERSED IN WATER, WITH A FORCE-PUMP AT ITS CENTRE AND HYDROSTATIC STREAM LINES — AND A CYLINDRICAL BAR OF IRON, MAGNETIZED, I. E., WITH A M. M. F. ACTIVE WITHIN IT AND MAGNETIC FLUX STREAM LINES. were supplied, the motion would soon cease. In the case of the ether, however, there being, by hypothesis, no friction, although energy would probably be required to set up the motion, yet, when once set up, no energy would be required to sustain it, and the motion should coiftinue indefinitely. This is similar to what we. find in the case of an actual steel magnet. The above theory is merely tentative. The real nature of magnetism may be quite different ; but, for practical purposes, assuming its correctness, since there is no knowledge as to the pole of the magnet from which the ether issues, it is assumed, as above stated, to issue from the north-seeking pole. 29. Fig. 20 represents, diagramatically, a tube provided at its centre with a rotary pump P, and immersed in water. If the pump were driven so as to force the water through the tube Digitized by VjOOQ LC MAGNETIC FLUX. 31 in the direction of the arrows; 1. e. y causing the water to enter the tube at S, and leave it at N> then stream lines would be produced in the surrounding water, taking curved paths, some of which are roughly indicated by arrows. Fig. 20A represents the application of this hypothesis to the case of a bar magnet of the same dimensions as the tube. Here the magneto-motive force of the magnet corresponds to the water-motive force of the pump in Fig. 20, and is hypothetically assumed to cause an ether stream to pass through the magnet in the direction indicated by the arrows ; namely, to enter the magnet at the south pole and issue at the north pole. These ether streams would constitute hypothetically the magnetic FIG. 21. — DISTRIBUTION OF FLUX ABOUT A STRAIGHT BAR MAGNET IN A HORIZONTAL PLANE, AS INDICATED BY IRON FILINGS. flux, and would pass through the surrounding space in paths roughly indicated by the arrows. The actual flux paths that would exist in the case of a uniformly magnetized short bar magnet are more nearly shown in Fig. 21. Here it will be noticed that the flux by no means issues from one end only of the magnet, re-entering at the other end. On the contrary, the flux, as indicated by chains of iron filings, issues from the sides as well as from the ends of the bar. The reason for this is evidently to be found in the fact, that each .of the particles or molecules of the iron, is, in all probability, a separate and independent magnet, and therefore must issue its own ether stream independently of all the rest. The effect is therefore not unlike that of a very great number of minute voltaic cells connected in series into a single battery, and the whole immersed in a conducting liquid where side leakage can exist. / Digitized by VjOOQ LC 32 ELECTRO-DYNAMIC MACHINERY. 30. The magnetic field, that is the space permeated by mag- netic flux, may be mapped out in the case of any plane section by the use of iron filings. For example, Fig. 21, before alluded to, as representing the flux of a straight-bar magnet, had its flux paths mapped out as follows : A glass plate, covered with a thin layer of wax, was rested horizontally on a bar magnet, with its wax surface uppermost. It was then dusted over with iron filings and gently tapped, when the iron filings arranged themselves in chain-forms, which are approximately those of FIGS. 22, A AND B. — MAGNETIC FIELDS BETWEEN PARALLEL BAR MAGNETS. the stream-lines of magnetic flux. A satisfactory distribution having been obtained in this manner, the glass plate was gently heated in order to fix the filings. On cooling, the filings were sufficiently adherent to the plate to permit it to be used as the positive from which a good negative picture can be readily obtained by photographic printing. 31. A modification of the above process was employed in the case of Figs. 22, A and B, shown above. Here a photographic positive was obtained by forming the field, in the manner pre- viously explained, on a sensitized glass plate in a dark room, instead of on a waxed plate ; and, after a satisfactory grouping of filings had been obtained under the influence of the field, exposing the plate momentarily to the action of light, as, for Digitized by VjOOQ LC MAGNETIC FLUX. 33 example, by the lighting of a match. The filings are then removed, the plate developed, and the negative so obtained employed for printing. 32. Magnetic flux may vary in three ways; namely, (1.) In direction. (2.) In intensity. (3.) In distribution. The direction of magnetic flux at any point can be readily determined by the direction assumed at that point, by the magnetic axis of a very small, delicately suspended compass needle. The compass needle always comes to rest as if threaded by the flux, which enters at its south pole, and leaves it at its north pole, thus causing the needle to point in the direction of the flux. Assuming that a compass needle may be represented FIG. 23. — HYDRAULIC ANALOGUE SHOWING ATTRACTION OF OPPOSITE POLES. by a little tube containing an ether force pump, the tube would evidently come to rest when the flux it produced passed through it in the same direction as the flux into which it was brought. That is to say, if the needle be brought into the neighborhood of a north pole, it will come to rest with its south pole pointing toward the north pole of the controlling magnet, since in this way only could a maximum free ether motion be obtained. If, however, the compass needle be held in the opposite direction; /. *., with its north-seeking pole toward the north-seeking pole of the magnet, the two opposed stream lines will,. by their reaction, produce a repellent force. These effects are generally expressed as follows : Like magnetic poles repel, unlike magnetic poles attract. Strictly speaking, this statement is not correct, since, what- ever theory of magnetism be adopted, it is the fluxes and not the poles which exercise attraction or repulsion. 33- Fig. 23 represents the action of the flux from a magnet upon a small compass needle, as illustrated by the hydraulic Digitized by VjOOQ IC 34 ELECTRO-DYNAMIC MACHINERY. analogy. The water is represented as streaming through the tube O N, and issuing at the end N, in curved stream lines. Suppose the small magnet, or compass needle S N, also has a stream of water flowing through it, entering at S l9 and leaving at N x . Then, if the compass needle be free to move about its centre of figure, it will come to rest when the stream from the large tube O JV, flows through the smaller tube from S x to N x that is, in the direction of its own stream. If, however, the small tube S x N x is not free to move, but is fixed with its end N x toward the end N of the larger tube, as FIG. 24. — HYDRAULIC ANALOGUE SHOWING REPULSION OF SIMILAR POLES. shown, in Fig. 24, then the opposite streams will conflict, and produce, by their reaction, the effect of repulsion between the tubes. 34. Magnetic flux possesses not only definite direction, but also magnitude at every point; that is to say, the flux is stronger nearer the magnet than remote from it. For example, considering a magnet as being represented by a tube with an ether force pump, the velocity of the ether flux will be a maxi- mum inside the tube, and will diminish outside the tube as we recede from it. The intensity of magnetic flux is generally called its magnetic intensity or flux density. Faraday, who first illustrated the properties of a magnetic field, proposed the term lines of magnetic force, and this term has been very generally employed. The term, however, is objectionable, especially when an attempt is made to conceive of magnetism as possessing flux density, or as varying in intensity at any point; for, in accordance with Faraday's con- ception, the idea of an increased flux would mean a greater number of lines of magnetic force traversing a given space. While this might be assumed as possible, still the conception that magnetism acts along lines, and not through spaces, is very misleading. An endeavor has been made to meet this Digitized by VjOOQ IC MAGNETIC FLUX. 35 objection by the introduction of the term tubes of force. A far simpler working conception is that of velocity of ether. that is, increased quantity passing per second, as suggested by the force-pump analogue. Here the increased flux density at any point would simply mean an increase of ether velocity at such poiiit. 35. Intensity of magnetic flux is measured in the United States, in units called gausses, after a celebrated German mag- netician named Gauss. A gauss is an intensity of one line of force, or unit of magnetic flux, per square centimetre of cross- sectional area, and is an intensity of the same order as that produced by the earth's magnetism on its surface. For ex- ample, the intensity of the earth's flux at Washington is about 0.6 gauss, with a dip or inclination of approximately 70°. Magnetic flux may be uniform or irregular. Fig. 25 A, shows a uniform flux distribution, as represented diagrammati- cally, by straight lines at uniform distances apart. That is to say, uniform intensity at .any point is characterized by rectan- gularity of direction in path at that point. Irregular intensity is characterized by bending, and the degree of departure from uniformity is measured by the amount of the bending. Irreg- ular flux density may be either converging, as at B, or diverging, as at C. Convergent flux increases in intensity along its path, and divergent flux diminishes. 36. When the flux paths are parallel to one another, the intensity must remain uniform. Thus, in Fig. 25 at A, let the area, A B CD, be 1 square centimetre, then the amount of flux which passes through it in this position, or, in our hydraulic analogue, the quantity of water which would flow through it in a given time, will be the same if the area be shifted along the stream line parallel to itself into the position E F G H. When the flux converges, as at B, in Fig. 25, then the amount of flux passing through the normal square centimetre I J K L, will, further on, pass through a smaller intercepting area, say one-fourth of a square centimetre M N O P, and consequently, the intensity at this area would be four times greater, and, in the hydraulic analogy, the same quantity of water passing per second, flowing through a cross sectional Digitized by VjOOQ LC 36 ELECTRO-DYNAMIC MACHINERY. area four times more constricted, will flow there with four times the velocity. When the flux diverges, as at C, the opposite effect is pro- duced. Thus the flux shown in the figure as passing through the area Q R S T 9 say one-fourth of a square centimetre, > ■ > — **» * ■ •+ ■ » » * — ► — *> — ► — * - » ■» > * *-» » ■ ■» ■ > — ► » ■- % ■■ » - » r »» » Uniform Flu* Intensity Unvarying B -*.. — p- — > — ► — *■ — ► — ► >-* ""---jo ---^ M Convergent Flux Intensity I nor easing v\U* O — » > — > — ► — *» Divergent Flux Intensity Diminishing ' FIG. 25. — VARIETIES OF FLUX. would, at U V WX y pass through one square centrimetre, at four times less density, or, in the case of the hydraulic analogy, at one-fourth of the velocity. 37. The existence of a magnetic flux always necessitates the expenditure of energy to produce it. In the case of the ether pump, assuming that energy is required to establish the flow through the tube, this energy being imparted to the ether, becomes resident in its motion, so that ether, plus energy of motion, necessarily possesses different properties from ether Digitized by VjOOQ IC MAGNETIC FLUX. 37 at rest. In the same way in the case of a magnet, the energy required to set up the magnetic flux; /". °°° 8 x 3-1416 = 0.5868 x io 7 ergs. = 0.5868 joule. 39. Just as in the electric circuit, the presence of an electric current necessitates the existence of an E. M. F. producing it. so in a magnetic circuit, the presence of a magnetic flux neces- Digitized by VjOCK 3** ELECTRO-DYNAMIC MACHINERY, sitates the existence of a magneto-motive force (M. M. F.) producing it. We know of but two methods by which a M. M. F. can be produced, viz. : (i.) By the passage of an electric current, the neighborhood of which is invested with magnetic properties; /. t. y surrounded by magnetic flux; (2.) As a property inherent in the ultimate particles of cer- FIG. 27. — GEOMETRICAL DISTRIBUTION OF FLUX PATHS ROUND A WIRE CARRYING A CURRENT. tain kinds of matter, possibly the molecules, of the so-called magnetic metals. The passage of an electric current through a long, rectilin- ear conductor, is attended by the production of a magnetic field in the space surrounding the conductor. The distribution of flux in this field, is a system of cylinders concentric to the conductor, and is directed clock-wise around the conductor, if the current be supposed to flow through the clock from its face to its back. This distribution is shown in Figs. 26, 27 and 28. Fig. 26 represents the distribution as obtained by iron filings. The density of the flux is roughly indicated by the density of the corresponding circles. Digitized by VjOOQ LC MAGNETIC FLUX, 39 40. Fig. 27 shows the geometrical distribution of the flux paths around a wire carrying a current, which is supposed to flow from the observer through the paper. Here a few of the flux paths are indicated by the circles, 1, 2, 3, 4 and 5, while the direction is shown by the arrows. The distribution of the flux is such that it varies in intensity, outside the wire, inversely as the distance from the axis of the wire, and the total flux between any adjacent pair of circles in the figure is the same, FIG. 28. — DIAGRAM OF RELATIVE DIRECTIONS OF MAGNETIC FLUX AND ELECTRIC CURRENT. for example, between 1 and 2, or between 4 and 5. Or, in the hydraulic analogue, the total flow of water per second, between any pair of adjacent circles is the same, as between the circles 2, 3, or 4, 5, the velocity diminishing as the distance from the axis of the wire. Fig. 28 represents the direction of the flux round the active conductor, the current flowing from the observer through the shaded disc. 41. The physical mechanism of the magnetic flux produced by a current is unknown, but if an electric current be assumed to be due to a vortex motion of ether in the active wire, the direction of which is dependent on the direction of the current through the wire, then such vortex motion will be accompanied by such a distribution of circular stream-lines in the ether, as is actually manifested, and, when the direction of the current through the conductor is changed, the direction of the stream- lines outside the conductor will also necessarily be changed. Digitized by VjOOQ LC 4Q ELECTRO-DYNAMIC MACHINERY. As the strength of the current through the wire increases, the velocity of the ether surrounding the wire increases; i. *., the intensity of the magnetic field everywhere increases. 42. If a conductor conveying a current be bent in the form of a circle as shown in Fig. 29, and a current, of say one ampere, be sent through the conductor, there passes through the loop so formed a certain number of stream-lines as repre- sented diagrammatically. If now, the current in the wire be t: >-' i- FIGS. 29 AND 30. — SINGLE LOOP OF ACTIVE CONDUCTOR, THREADED WITH FLUX, AND DOUBLE LOOP WITH M. M. F. DOUBLED. doubled, that is increased to two amperes, the flux intensity everywhere will be doubled. The same effect, however, can be practically obtained by sending one ampere through the double loop, shown in Fig. 30, provided the two turns lie very close together. Magnetic flux through a loop, will depend, therefore, upon the number of ampere-turns, so that, by wind- ing the loop in a coil of many turns, the flux produced by a single ampere through the coil may be very great. The M. M. F. produced by a current, therefore, depends upon the number of ampere-turns. 43. The unit of M. M. F. may be taken as the ampert-turn y and it frequently is so taken for purposes of convenience. The fundamental unit, however, of M. M. F., in the United States, is the gilbert, named after one of the earliest magneticians, Dr. Gilbert, of Colchester. The gilbert is produced by — of a 47T Digitized by VjOOQ LC MAGNETIC FLUX. 4* C. G. S. unit current-turn, and, since the C. G. S. unit of current is ten amperes, the gilbert is produced by — ampere-turn (0.8 approximately, more nearly 0.7958). It is only necessary, therefore, to divide the number of ampere-turns in any coil of FIG 31. — DISTRIBUTION OF FLUX IN PLANE OVER A HORSE-SHOE MAGNET. wire by 0.8, that is to multiply the number of ampere-turns by 1.25, more nearly 1.257) to obtain the M. M. F. of that coil expressed in gilberts. 44. Figs. 31 to 42 are taken from actual flux distributions as obtained by iron filings, and represent a series of negatives or positives secured by the means already described. A study of FIG. 32. — DISTRIBUTION OF FLUX IN PLANE OVER A HORSE-SHOE MAGNET. such flux-paths assists the student to mentally picture the flux distributions which occur in practice. Figs. 31 and 32 are the respective positive and negative photographic prints taken in the case, of a horse-shoe magnet. Here the filings are absent in a region outside the magnet in the neighborhood of the poles N S. The cause of this is as fol- lows : the fields were obtained by sprinkling iron filings over Digitized by VjOOQ IC 42 ELECTRO-DYNAMIC MACHINERY. a smooth glass surface; the tapping of the surface necessary to insure the arrangement of the filings under the influence of the magnetic flux, has caused an accumulation of filings around these poles at the expense of the gap immediately in front of the poles which would otherwise be more fairly filled. FIG. 33. — DISTRIBUTION OF FLUX BY IRON FILINGS IN PLANE OVER POLES OF ELECTRO-MAGNET. 45. The student should carefully avoid being misled by the supposition that the relative attractive tendencies of the iron filings in such diagrams represent the corresponding densities of the magnetic flux, for the reason that in a uniform mag- netic flux such as shown at A, in Fig. 25, there is no attrac- tion of iron filings, whatever its intensity, although, of course, FIG. 34. — DISTRIBUTION OF FLUX BY CUT IRON WIRE IN PLANE OVER POLES OF ELECTRO-MAGNET. a directive tendency still exists. In order that there should be any attractive tendency, in contradistinction to a mere directive tendency, it is necessary that the intensity of the magnetic flux shall vary from point to point; or, in other words, that the flux shall be convergent. The greater the degree of convergence the greater the attractive force. Consequently, variations of flux intensity as indicated by iron Digitized by VjOOQIC MAGNETIC FLUX. 43 filings always exaggerate the appearance of flux density. Generally speaking, it is only the directions assumed by the filings in such diagrams, as indicative of the directions of the flux, which can be regarded as trustworthy. The neglect of this consideration has given rise to a popular belief that magnetic streamings occur with greater density at points, than at plane or blunt surfaces, which is not the case. There must necessarily be a rapid convergence or divergence of mag- FIG.,35. — PLAN AND SIDE ELEVATION OF MAGNET EMPLOYED IN CONNECTION WITH FIGS. 36 AND 37. netic flux at points, although the maximum density may not be very great. Owing to this convergence, iron filings, particles, nails, etc., are attracted more powerfully at such points, even though the uniform intensity of flux at plane surfaces in the vicinity may be greater. 46. Fig. 33 shows the distribution of magnetic flux as obtained by iron filings in a horizontal plane over the vertical poles of an electro-magnet. Here the flux-paths pass in straight lines between the nearest points of the adjacent poles, and in curved lines over all other parts of the plane. If we imagine, following the hydraulic analogue, that water streams proceed from minute apertures in one of the poles, and that Digitized by VjOOQ IC 44 ELECTRON YNAMIC MACHINERY, the magnet is immersed in water, then the stream-lines so pro- duced in the water as it emerges from pole N y and enters through pole S 9 will be the same as is indicated by the iron i&i '"'<■) 1§ FIG. 36. — DISTRIBUTION OF FLUX BY IRON FILINGS IN PLANE OVER MAGNET SHOWN IN FIG. 35, WITH MAGNET PRESENTED VERTICALLY. filings. Fig. 34 shows a similar distribution of flux over the poles of the same electro-magnet, where short pieces of fine soft iron wire were used in place of the iron filings. FIG. 37. — DISTRIBUTION OF FLUX BY IRON FILINGS IN PLANE OVER MAGNET SHOWN IN FIG. 35, WITH MAGNET PRESENTED HORIZONTALLY. Here the flux-paths have practically the same distribution as in the preceding case. Figs. 36 and 37 show the distribution of flux by iron filings in a horizontal plane over the poles of the magnet represented in Fig. 35, the magnet being presented vertically in Fig. 36, Digitized by VjOOQ LC MAGNETIC FLUX 45 and horizontally in Fig. 37, to the plane. Here the general ^distribution of flux between the polar surfaces is rectilinear. %1^ FIG. 38. — FLUX-PATHS BETWEEN DISSIMILAR POLES. Fig. 38 illustrates the flux distribution attending the approach of what are called unlike poles. Here the ether FIG. 39. — FLUX-PATHS BETWEEN SIMILAR POLES. streams we assume to issue from JV, in entering the magnet S, take the paths indicated. Fig. 39 illustrates the flux distribution attending the Digitized by VjOOQ IC 4 6 ELECTR0.DYNAM1C MACHINERY. approach of what are called like poles. Here the hypothetical ether streams issuing from JV 9 N, impinge, as shown, and pro- FIG. 40. — FLUX-PATHS BETWEEN TWO PARALLEL BAR MAGNETS, SIMILAR POLES ADJACENT. duce a neutral line, A A, corresponding to slack water in the hydraulic analogue. FIG. 41. — FLUX-PATHS BETWEEN TWO PARALLEL BAR MAGNETS OPPOSITE POLES ADJACENT. Fig. 40 shows the distribution of flux in the case of two* straight bar magnets laid side by side with like poles opposed. Digitized by VjOOQ LC MAGNETIC FLUX. 47 The imaginary ether streams again oppose and the neutral line B £, is produced as shown. Fig. 41 shows the distribution of magnetic flux in the case of two straight bar magnets, laid side by side, with unlike poles opposed. Here, according to hypothesis, some of the ether streams issuing from each magnet, pass back through the other magnet, the remainder closing their circuit through FIG. 42. — FLUX-PATHS SURROUNDING ANOMALOUS MAGNBT. the air outside. A curious central region between the mag- nets, bounded by curves resembling hyperbolas is shown at C, where, by symmetry, no ether motion penetrates, and thus corresponding, in the hydraulic analogue, to calm water. Fig. 42 shows the distribution of flux over the surface of what is commonly called an anomalous magnet, that is a magnet having two similar poles united at its centre; or, in other words, having two separate magnetic circuits. Here the dis- tribution of flux is similar to that in Fig. 40, where like poles are approached. Digitized by VjOOQ IC CHAPTER IV. NON-FERRIC MAGNETIC CIRCUITS. 47. As we have already seen, magnetic flux always flows in closed paths, or forms what is called a magnetic circuit. The quantity of magnetic flux in a magnetic circuit depends not only upon the magneto-motive force, but also on the disposition and nature of the circuit. For example, it is not to be sup- posed that the flux produced by the 12 ampere-turns (15.084 gilberts) in the right-handed coil or helix of Fig. 43, by one ampere flowing through the twelve turns shown, would be FIG. 43. — RIGHT-HANDED HELIX OF 12 TURNS CARRYING ONE AMPERE. exactly the same, either in magnitude or distribution, as the flux from a single turn carrying 12 amperes, although the M. M. F. would be the same in each case. Just as in the case of an electric circuit, the current produced by a given E. M. F. depends on the resistance of the circuit, so in the case of a magnetic circuit, the magnetic flux produced by a given M. M. F. depends on a property of the circuit called its magnetic reluctance, or simply its reluctance. Magnetic reluctance, therefore, is a property corresponding to electric resistance, and is sometimes defined as the resist- ance of a circuit to magnetic flux. The resistance, in ohms, of any uniform wire forming portion of an electric circuit is equal to the resistivity, or specific resist- ance, of the wire, multiplied by the length of the wire, and divided by its cross-sectional area. In the same way, the reluctance, in oersteds, of any uniform portion of a magnetic circuit, is equal to the reluctivity, Or specific magnetic resistance of the portion, multiplied by its length in centimetres, and divided by its cross sectional area in square centimetres. The reluctivity of 48 Digitized by VjOOQ LC NON-FERRIC MAGNETIC CIRCUITS. 49 air, wood, copper, glass, and practically all substances except iron, steel, nickel and cobalt, is unity. Strictly speaking, the reluctivity of the ether in vacuous space is unity, but the dif- ference between the reluctivity of vacuum and of all non- magnetic materials is, for all practical purposes, negligibly small. Thus, the reluctance of a cylinder of air space of 10 cms. long and 2 sq. cms. in cross-sectional area, is 5 oersteds. 48. The reluctance of a circuit is measured in units of reluct- ance called oersteds. An oersted is equal to the reluctance of a cubic centimetre of air (or, strictly speaking, of air-pump vacuum) measured between opposed faces. Having given the reluctance of a magnetic circuit, and its total M. M. F., the flux in the circuit is determined in accord- ance with Ohm's law; that is = — where &, is the flux in webers, SF, is the magneto-motive force in gilberts, and (ft, the reluctance in oersteds. It may afford assistance to con- volts trast the well-known expression: amperes = -r — , with the gilberts corresponding magnetic expression, webers = oersteds. 49. The unit of magnetic flux, in the United States, is called the weber, and is equal to the flux which is produced by a M. M. F. of one gilbert acting through a reluctance of one oersted, cor- responding in the above expression to the ampere, the unit of electric flux, which is the electric flux or current produced by an E. M. F. of one volt through a resistance of one ohm. For example, if an anchor ring of wood, such as is represented in Fig. 44, have a cross section of 10 sq. cms. and be uniformly wrapped with insulated wire, then when the current passes through the winding, the magnetic circuit will be entirely con- fined to the interior of the coil or solenoid, and no magnetic flux will be perceptible in the region outside it. This is the only known form of magnetic circuit in which the flux-paths can be confined to a given channel. These flux-paths are all circular, and possess the same intensity around each circle. If the mean circumference of the ring be 60 cms., the reluct- • 60 ance of the magnetic circuit will be approximately — = 3^K 50 ELECTRO-DYNAMIC MACHINERY. 6 oersteds, as in the similar case of electric resistance. If the number of turns in the winding be 200, and the exciting current steadily maintained at four amperes, the M. M. F. in the magnetic circuit will be 800 ampere-turns, or 1,005.6 gilberts. From this the total flux through the ring will be -—, - = 167.6 webers. fig. 44.- -9E6TI0NS OF WOODEN RING UNIFORMLY WRAPPED WITH INSULATED WIRE CARRYING A CURRENT. 50. Besides the case of the anchor ring, represented in Fig. 44, the magnetic circuit of which, being entirely confined to the interior of the coil, permits its reluctance to be readily calculated, and the flux to be thus arrived at, another case, almost as simple, is afforded by a long straight helix of length / cms., uniformly wrapped with «, turns per cm. or N -=. I n, turns in all. Such a helix, when excited by a current of / amperes, develops a M. M. F. of n /ampere-turns, or 1.257 n I gilberts in each centimetre, or 1.257 N I gilberts, for the total M. M. F. The magnetic circuit of such a solenoid is roughly repre- Digitized by VjOOQ IC NON-FERRIC MAGNETIC CIRCUITS. S 1 sented in Fig. 20 A. An inspection of this figure will show that flux passes through the interior of the helix in parallel streams, until it reaches a comparatively short distance from the ends, when it begins to sensibly diverge, and, emerging into the surrounding space, is diffused through widely divergent paths. That is to say, the magnetic circuit is characterized by two distinct regions; namely, that within the coil, where the flux is uniform, and, except near the ends, of a maximum intensity, and that outside and beyond the ends of the coil, where the flux is divergent and greatly weakened in intensity. 51. In the case of a long, straight, uniformly-wrapped helix, the reluctance of the circuit may be considered as consisting of two distinct portions; namely, a straight portion occupying the interior of the coil and lying practically between the ends, and a curved or diffused portion exterior to the coil. The reluctance of the first, or interior portion, will be practically — oersteds, where a, is the cross sectional area of the interior of the coil in square cms. and /, the length of the coil in cms., or, more nearly, the reduced length of the non-divergent flux. It will be seen, therefore, that the interior of the coil behaves like a straight wire carrying electric flux, since it practically confines the flux to its interior, and, this particular portion of the magnetic circuit is similar to the case of the anchor ring above referred to, where the magnetic flux is confined to the interior of the ring. Since the external circuit is diffused, its reluctance cannot be so simply expressed. Its value, however, may obviously be dealt with as follows : although the mean length of the flux- paths outside the coil is greater than in the interior portion, yet the area of cross section of the circuit is enormously extended. It would appear, therefore, that in the case of an indefinitely long straight coil, the external reluctance becomes negligibly small compared with the internal reluctance, and may be left out of consideration. In such a case, therefore, the flux established becomes - 1.257 l n I r $ = — ±L = l 257 n I a webers : Digitized by VjOOQ IC 5 2 ELECTRON YiVAMIC MA CHINER Y. and, since, within the coil, this flux passes through a cross sec- tional area of a square centimeters, the interior intensity will be _ 1.257 n I a T $ = — ±L = 1.257 n I gausses. Strictly speaking, therefore, this is the intensity of flux within an indefinitely long straight helix, and is approximately the intensity within helices which have lengths more than 20 times their diameter. 52. We have now discussed two cases of non-ferric circuits, whose reluctance is readily calculated ; namely, a closed cir- cular coil and a long straight helix. In all other cases, the reluctance of a magnetic circuit is much more difficult to compute, although the fundamental relations remain unchanged. When the magnetic circuit is non-ferric, although the reluctivity of the circuit always equals unity, yet, owing to the difficulty of determining the exact paths followed by the diver- gent flux, the reluctance is difficult to determine. Most practical magnetic circuits, however, are composed either entirely, or mainly, of iron. At first sight, the intro- duction of iron into the circuit would appear to make the reluctance more difficult to determine, because the reluctivity of iron not only varies greatly with different specimens, but also with its hardness, softness, annealing, and chemical com- position. Moreover, the apparent reluctivity of iron varies markedly with the density of the flux passing through it. Iron, when magnetically saturated, possesses a reluctivity equal to that of air; while, as we have seen, al low intensities, the reluctivity is much smaller, and may be several thousand times smaller. Since, however, ferric circuits, as ordinarily employed, practically confine their flux-paths to the substance of the iron, and, since the reluctance of the iron is so much less than the reluctance of the alternative air path outside, the air flux may usually be neglected. Even where, owing to the reluct- ance of the air gaps in the circuit, such as in the case of dynamos and motors, a considerable amount of magnetic leakage Digitized by VjOOQIC NON-FERRIC MAGNETIC CIRCUITS. 5$ or diffusion may take place through the surrounding air, yet it is preferable to regard this leakage as a deviation from the iron circuit, which may be separately treated and taken into account, and that the flux passes principally through the iron. For these reasons, ferric or aero-ferric circuits, at least in their practical treatment, are simpler to determine and compute than non-ferric circuits, since, although their reluctivity is variable at different points, yet the geomet- rical outlines of the flux-paths can be regarded as limited, and the reluctance of these paths can be readily determined approximately. 53. Magnetizing force may be defined as the space rate at which the magnetic potential descends in a magnetic circuit. Since the total fall of magnetic potential is equal to the M. M. F. in the circuit, just as the total "drop" in a voltaic circuit is equal to its E. M. F. Consequently, the line integral or sum of magnetizing force in a magnetic circuit must be equal to the M. M. F. in that circuit. In other words, if we multiply the rate of descent in potential by the distance through which that rate extends, and sum all such stages, we arrive at the total descent of magnetic potential. For instance, in Fig. 44 the total difference of magnetic potential is 1,005.6 gilberts, which, by symmetry, is uniformly distributed round the entire circuit. Since the mean length of this circuit is 60 cms. the rate of fail of potential is ? - — = 16.76 giiberts-per-centimetre all round 60 the ring, and this is, therefore, the magnetizing force, or, as it is sometimes called, the magnetic force. This magnetizing force is usually represented by the symbol 3C, and, when no iron or magnetic metal is included in the circuit, is numerically iden- tical with the flux density (ft, so thatJC, is expressed in gilberts- per-centimetre. The term magnetizing force was adopted from the old conception of magnetic poles ; for, if a pole o{ unit strength could be introduced into a flux of intensity 3C gausses, the mechanical force exerted upon the pole would be 3C dynes, directed along the flux-paths. In any magnetic circuit, if we divide the M. M. F. in gilberts, by *he length of a flux-path, we obtain the average value of the magnetizing force (or flux density in the absence of iron). Thus, in Fig. 21, if the long Digitized by VjOOQ IC 54 ELECTRO-DYNAMIC MACHINERY. helix there represented, has a M.M. F. of 5,000 gilberts, and a particular flux-path has a length of 500 cms., the mean magnet- c OOO izing force, will be - = 10 gilberts-per-centimetre, and the mean flux density will be 10 gausses, if there is no iron in the circuit. If there is iron, the mean prime flux density or magnet- izing force, will still be 10 gilberts-per-centimetre, but the flux density established in the circuit will be greatly in excess of 10 gausses. Digitized by VjOOQ IC CHAPTER V. FERRIC MAGNETIC CIRCUITS. 54. We will now proceed to study the phenomena which occur when iron is introduced into a magnetic circuit, as for example, into the circuit of the. closed circular coil shown in Fig. 44, the mean interior circumference of which is 60 cms., and the mean cross sectional area 10 sq. cms. We . have seen that if this ring be excited with 800 ampere-turns, or 1005.6 gilberts, the flux through the ring will be 167.6 webers; or, since the cross section of the ring is ten square centimetres, • 167 6 the intensity will be — — = 16.76 gausses, and this inten- sity would remain practically unchanged if the substance of the ring were copper, brass, lead, zinc, wood, glass, etc. When, however, the ring is made of iron or steel, a very marked change takes place ; the flux instead of being 167.6 webers, becomes, say, 170,000 webers, with a corresponding increase in intensity. This increase of flux in the circuit must either be due to an increase in the M. M. F., or to a diminution in the reluctance. It is usual to consider that iron conducts mag- netic flux better than air; or, in other words, has a greater mag- fietic permeability than air. This idea corresponds to a reduc- tion of reluctance similar to the reduction of resistance in an electric circuit. Although generally accepted, this conception is manifestly incorrect ; for if the increased flux, due to the presence of iron in the ring, disappeared immediately on the removal of the M. M. F., there would be no preponderance of evidence in favor of either hypothesis. But the magnetic flux does not entirely disappear on the cessation of the prime M. M. F. On the contrary, in Aie case of a closed iron ring, the greater portion of the flux remains in the condition called residual magnetism. 55. It is evident, therefore, since M. M. F. is necessary to maintain the residual magnetic flux in the iron, that this 55 Digitized by VjOOQ IC 56 ELECTRO-DYNAMIC MACHINERY, M. M. F. is the cause of the increase in magnetic flux when the prime M. M. F. is applied, and that, therefore, the increased flux cannot be due, except, perhaps, in a very small degree, to any change in the reluctivity of the medium, but to the establishment of a M. M. F. in the iron itself under the influ- ence of the magnetizing flux. It is now almost certain that the ultimate particles of the iron, the molecules, or the atoms, are all initially magnets ; i. e., inherently possess M. M. Fs. and magnetic circuits. The origin of this molecular magnetism in iron is, however, not yet known. In the natural condition, all the separate magnets of which iron is composed, are dis- tributed indifferently in all directions, so that their circuits neutralize one another and produce no appreciable external effects. Under the influence of a magnetizing flux, these mole- cular magnets tend to become aligned, and to break up their original groupings. As they become aligned, and their M. M. Fs. become similarly directed, they are placed in series, and their effects are rendered cumulative, so that they exercise an increasing external influence, and an extending external flux. Or, taking ' the hydraulic analogue already referred to, and regarding each separate molecular magnet as a minute ether pump, as all the ether pumps are brought into line, the streams they are able to direct are increased in velocity, and are, there- fore, carried further into the surrounding space. Conse- quently, the flux produced in the magnetic ring shown in Fig. 44, when furnished with an iron core, may be regarded as aris- ing from two distinct sources of M. M. F. ; namely, (i.) The prime M. M. F. y or that due to the magnetizing current which produces the flux through the circuit and sub- stance of the iron, the value of which is practically the same as though the core were of wood or other non-magnetic material. This flux may oe called the prime flux and possesses a corresponding prime intensity. In the case considered, the prime intensity or magnetizing flux density is 16.76 gausses. This magnetic intensity, acting upon the molecules of the iron, produces: (2.) The induced M. M. F. y which may be called the aligned or structural M. M. F. y and depends for its magnitude not only upon the quality of the iron, but also upon the intensity of the prime flux. The harder the iron, and the greater its mecham- Digitized by VjOOQ LC FERRIC MAGNETIC CIRCUITS. 57 cal tendency to resist molecular distortion, the greater must be the prime intensity or the magnetic distorting power, in order to bring about the full structural M. M. F. When the prime intensity has reached such a magnitude that all the separ- ate molecular magnets in the iron are similarly aligned, the iron is said to be saturated, and the M. M. F. it produces is a maximum, and, on the removal of the prime M. M. F. the structural M. M. F. will, in the case of a closed ring, largely remain, especially if the ring be of hard iron or steel. If, on FIG. 45. — IRON RING PROVIDED WITH AIR-GAP, AND WOUND WITH WIRE. the contrary, the ring be of soft iron, and have an air-gap cut in it, the structural M. M. F. may largely disappear. The relation between the structural M. M. F. and its flux, and the prime M. M. F. and the intensity which produces it, is complex, and can only be ascertained by experimental observation. 56. Fig. 45 represents the same iron ring with a saw-cut or air-gap at A, having a width of 0.5 cm. The reluctance of this air-gap, which, neglecting diffusion, has a length of 0.5 cms. and a cross-section of 10 sq. cms. is -^ = 0.05 oersted. If the total structural M. M. F., established in the ring under excitation, be 180,000 gilberts, then, immediately on the with- Digitized by VjOOQ LC 58 ELECTRO-DYNAMIC MACHINERY. drawal of the prime M. M. F., the residual flux through the circuit will be — ^ — = 30,000 webers. Where this flux passes through the reluctance of the air-gap there will be established a C. M. M. F., just as in the electric circuit where a current of / amperes passes through a resistance of R, ohms, there is established a C. E. M. F. oi I R volts. So that the C. M. M. F. has in this case the value, F = $ R = 30,000 x 0.05 = 1,500 gilberts. This C. M. M. F. represents a mean demagnetizing force of —■ — = 25 gilberts-per- centimetre, through the iron circuit. If this intensity of de- magnetizing force is sufficient to disrupt the structural align- ment of the molecular magnets, the residual magnetism will disappear. If, however, the intensity be less than that which the hardness of the iron requires to break up its structure, the residual magnetism will be semi-permanent. Even though it be admitted that the preceding represents the true condition of affairs, and though it is the only existing hypothesis by which the phenomena of residual magnetism can • be accounted for, nevertheless, for practical computations connected with dynamo machinery, it is more convenient to assume that there is no structural M. M. F. in iron, and that the difference in the amount of flux produced in ferric circuits is a consequence of decreased reluctance in the iron; or, in other words, that iron is a better conductor of magnetism. We will, therefore, in future, adopt the untrue but more con- venient hypothesis. 57. The reluctivity of iron may be as low as 0.0005, but varies with the flux density ; that is to say, the reluctance of a cubic centimetre of iron, measured between parallel faces, may be as low as 0.0005 oersted. 58, .The fact has been established by observation, that in the magnetic metals, within the limits of observational error, a linear relation exists between reluctivity and magnetizing force. That is to say, within certain limits, as the magnetizing force brought to bear upon a magnetic metal increases, the apparent reluctivity of the metal increases in direct proportion. Thus, taking the case of soft Norway iron, its reluctivity, at a mag- Digitized by VjOOQ IC FERRIC MAGNETIC CIRCUITS. 59 netizing force of 4 gilberts-per-centimetre, or prime magnetic intensity of 4 gausses, may be stated as 0.0005. Increasing the magnetizing force, the reluctivity increases by 0.000,057 OJOU —7 . Ordinary SampU of Dynamo Catt.lrofi(K«nnolly>y-d.0026 , + 0.000093' JC . Sampla of Dynamo Wrought Iron X=0.0OO4+ 0.000057 JC / 1 III. Samjrfa of Annoalod Norway Iron r-0.0003+ 0.000057 JC llV. « Soft Iron (Stol«tow)9'-0.0002 + 0.000056 JC —TV. h Norway Iron ( Rowland)*** 0.0001 + 0.000059 JC / - • ^ ^0.007 > \ O V UJ DC \ O -J \ S € Ul \ ^ S y^ Z ^ ^ IP COl ■ ( > 1 ) i > I \ 1 > 6i > • > 7 \ X »► MAGNETISING FORCE JC/ =21.67 gilberts-per-centimetre, and the intensity, 21.67 gausses; while, if the outer circumference be I 2*>7 -62 cms., the intensity at that circumference will be * — 62 ~~ 20.27 gausses. Since, however, all such existing differences of intensity can be made negligibly small, by sufficiently increas- ing the ratio of the size of the ring to its cross section, we may, for practical purposes, omit them from consideration. 61. Suppose now the core of the ring be composed of soft Norway iron instead of wood; then from the preceding curves, or the equation, v = 0.0004 -f- 0.000,057 JC, we find that at this mean intensity of 3C = 20.95 v = 0.0004 + o. 001 194 = 0.001594, or about - — th of that of air. The mean length of the cir- Digitized by VjOOQ IC ' 62 ELECTRO-DYNAMIC MACHINERY. cuit being 60 cms., and its area, as before mentioned, 10 sq. cms., its reluctance, under these circumstances, will be — x 10 0.001594 = 0.009564 oersted, and the flux in the circuit 1 5 = 131,430 webers, with an intensity of- — 0.009564 ° r° ' '10 13,143 gausses. 62. If the core of the ring instead of being of soft Norway iron be made of cast iron, the reluctivity, at JC = 20.95, would be approximately, 0.0046, and the reluctance of the circuit 0.0276 oersted, making the total flux 45,540 webers, with an intensity of 4,554 gausses, or about three times less than with soft Nor- way iron. The practical advantages, therefore, of construct- ing cores of soft Norway iron, rather than of cast iron, is man- ifest, when a high intensity is required. 63. It is important to remember that the entire conception of metallic reluctivity is artificial, and that although very con- venient for purposes of computation, yet as already pointed out, it is incompetent to deal with the case of residual magnetism. Thus, if the prime M. M. F. from an iron ring be withdrawn, we should expect the flux to entirely disappear, whereas we know that a large proportion will generally remain. Since, however, electro-dynamic machinery rarely calls residual magnetism into account, the reluctivity theory is adequate for practical pur- poses beyond critical magnetizing forces. 64. As another illustration, let us consider a very long rod of iron, wound with a uniform helix. Here, as we have already seen, disregarding small portions near the extremities, the intensity may be regarded as uniform within the helix. Since the reluctance of the external circuit may be neglected, this flux density is 1.257 n i, gausses, where n, is the number of loops in the helix per centimetre of length, and /, is the exciting current strength in amperes. Or, regarding the intensity as being numerically equal to the gradient of mag- netic potential, which changes steadily by 1.257 n /, per centi- metre (this being the number of gilberts added in the circuit per centimetre of length, the fall of potential or drop in the Digitized by VjOOQ LC FERRIC MAGNETIC CIRCUITS. 63 external circuit being negligible), the gradient, within the helix, is 1.257 n i gausses as before. A rod of Norway iron 1 metre long and 2 cms. in diameter, wound with twenty turns of wire to the centimetre, carrying a current of 1 ampere, would, at this magnetizing force, have an intensity in it of approximately 1.257 X 20 x 1 = 25.14 gausses. The reluc- tivity of Norway iron would be by the preceding formula v = 0.0004 + 0.000,057 x 25.14 = 0.001833 or about — th 500 of air. The length of rod being 100 cms., and its cross section 3.1416 square cms., the reluctance would be approximately ™ X 0.001833 = 0.05836 oersted. The total M. M. F. 3* I 4 I o being 100 x 20 x 1 = 2,000 ampere-turns == 2,514 gilberts. The flux in the circuit, assuming that the reluctance of the air path outside the bar may be neglected, is, approximately, 2 CIA A.T OTO — ° * = 43,070 webers, with an intensity of — ' = 13,710 0.05830 3- 14 16 gausses. 65. In cases where the flux is confined to definite paths, as in a closed circular coil, or in a very long, straight, and uni- formly wrapped bar, the preceding calculations are strictly applicable. When, however, an air-gap is introduced into the closed ring, that is, when its circuit becomes aero-ferric, the results begin to be vitiated, partly owing to the influence of diffusion, and partly to the results of the C. M. M. F. which is established at the air-gap. As the length of the air- gap increases, the degree of accuracy which can be attained by the application of the formula diminishes, but in dynamos, the aero-ferric circuits are in almost all cases of such a char- acter, that the degree of approximation, which can be reached by these computations, is sufficient for all practical purposes; for, while it is impossible strictly to compute the magnetic circuit of a dynamo by any means at present within our reach, yet the E. M. F. of dynamos, and the speed of motors, can be predicted by computation within the limits of commercial requirements. 66. If the ring of Fig. 45 be provided with a small air-gap of 0.5 cm. in width, the intensity in the circuit, before the intro- Digitized by VjOOQ IC H ELECTRO-DYNAMIC MACHINERY. duction of the iron core, will be practically unchanged by the existence of the gap, that is to say, with the same 1,000 ampere- turns, or 1,257 gilberts of M. M. F., the prime intensity exist- ing in the ring will be practically 20.95 gausses. In the air- gap itself, the intensity will be less than this, owing to lateral diffusion of the flux; but, neglecting these influences, we may consider the intensity to be uniform. Now, introducing a soft, Norway iron core into the ring, the iron is subjected to an intensity of approximately, 20.95 gausses throughout the cir- cuit. The reluctivity of the iron at this intensity, is, as we have seen, 0.001596. The length of the circuit in the iron will be 59.5 cms., and its cross section 10 sq. cms., making the ferric reluctance $2JL x 0.001594 = 0.009484 oersted. The reluctance of the air-gap, neglecting the influence of lateral o. 5 diffusion, will be — x 1 =0.05 oersted, and the total reluct- 10 •* ance of the circuit therefore, will be 0.009484 + 0.05 = 1 2^7 0.059484 oersted. The flux in the circuit will be — ' J = 0.059484 21,130 webers, and the- intensity in the iron, 2,113 gausses. The existence of the air-gap has, therefore, reduced the flux from 131 kilowebers to 21 kilowebers. 67. In practical cases, however, the problem which presents itself is not to determine the amount of flux produced in a magnetic circuit under a given magnetizing force, but rather to ascertain the M. M. F., which must be impressed on a cir- cuit in order to obtain a given magnetic flux. When the total required flux in a circuit is assigned, the mean intensity of flux in all portions of the circuit is approximately determinable, being simply the flux divided by the cross section of the circuit from point to point. What is required, is the reluctivity of iron at an assigned flux density and this we now proceed to determine. From the equations, v = a -f- b 3C, and (B = — , correspond- ing in a magnetic circuit, to i = in the electric circuit, /, being the electric flux density or amperes-per-sq.-cm. and p, the resistivity, we obtain, v = — Digitized by VjOOQ LC FERRIC MAGNETIC CIRCUITS. 65 This equation gives the reluctivity of any magnetic metal for any value of the flux density (E passing through it, when the value of the constants a and b, have been experimentally determined. The values of v, so obtained are only true for reluctivities beyond the critical value, where the linear relation expressed in the equation v = a + b 3C commences. 68. The following table gives the values of the reluctivity constants a and b y for various samples of iron : Sample. m b Observer. Soft Iron • . 0.000,2 0.000,056 Stoletow. Norway Iron 0.000,1 0.000,059 Rowland. Sheet Iron, 0.000,2375 0.000,0595 Fessenden. " " 0.000,2275 0.000,0654 •' " " 0.000,3325 0.000,064 " " " 0.000,213 0.000,05605 " Cast Steel 0.000,45 0.000,05125 " ••« " 0.000,314 0.000,0563 " Mitis Iron 0.000,25 0.000,0575 " Cast Iron, 0.001,031 0.000,129 " Improved Cast Iron, . . 0.000,9025 0.000,106 " Wrought Iron, .... 0.000,22 0.000,058 Hopkinson. Dynamo Wrought Iron, . . 0.000,4 0.000,057 Kennelly. " Cast Iron, . . 0.002,6 0.000,093 " Annealed Norway Iron, 0.000,3 0.000,057 " 69. Fig. 47 shows curves of reluctivity of various samples of iron and steel at different flux densities. The descending branches are of practically little importance in connection with dynamo-electric machinery. They are included in the curves, however, in order to bring these into coincidence with actual observations. It will be seen, that while the reluctivity of Norway iron is only 0.000,5 at 8 kilogausses, that of cast iron is commonly about 0.010, or twenty times as great. 70. In order to show the application of the above curves of reluctivity, we will take the simplest case of the ferric circuit; namely, that of a soft Norway iron anchor ring, shaped as shown in Fig. 44, of 10 square centimetres cross section and 60 cms. mean circumference, uniformly wrapped with insulated wire. If it be required to produce a total flux of 80 kilowebers in this circuit, the intensity in the iron will be 8 kilogausses, Digitized by VjOOQ LC 66 ELECTRO-DYNAMIC MACHINERY. 0.011 f m w b ** 0.0D /, 0.010 / /) / // // -• — • \ / / X \ 1 1 & i // f _3 \ J 7 , \ 1 // 2 V 1 / f l\ / ,i \ ^ , w, , / 1, II IV, III, tamp ampl e of ( 98 Of C ast v\ :asi i ougl ron t iror (m tit) // V, VI, " " < rdinar nnea < y dy »d N tamo jrway wrou Iron jhtii on / // / // / / / / 7 \ > '/ / s \ C J S i i 4 I i i I 1 ) 1 L 1 8 1 3 H i i I a 17 ,18 (ft Kilogausse8 Flux Density in Iron FIG. 47. — CURVES OF RELUCTIVITY IN RELATION TO FLUX DENSITY. and, by following the curve for Norway iron, in Fig 47, it will be seen that its reluctivity at this density is 0.000,5. The re- 60 luctance of the circuit, therefore, will be — X 0.000,5 = °-°°3 10 Digitized by VjOOQ LC FERRIC MAGNETIC CIRCUITS. 67 oersted, and the M. M. F. necessary to produce the requisite magnetic flux will be *F = #== 108,700 webers, or an intensity of 9,058 gausses. The magnetic attraction between the surfaces per-square- centimetre, would, therefore, be 2lJ! ZL-i _ 3 264,000 25.133 °' dynes, or 3,331 grammes weight, or 7.342 lbs. weight; and, since the total polar surface amounts to 24 square centimetres, the total attractive force exerted between and across them is 176.2 lbs. weight. The effect of introducing cast iron instead of wrought iron into the magnetic circuit, keeping the dimen- sions and M. M. F. the same, has, then, been to reduce the total pull from 620.64 lbs. to 176.2 lbs., or 71.6 per cent. 77. If now an air-gap be placed in the circuit at R lt and R^ of half aninch (1.27 cm.) in width, as in Fig 49, two results will follow; viz., Digitized by VjOOQ IC 72 ELECTRO-DYNAMIC MACHINERY. (i.) A greater reluctance will be produced in the circuit. (2.) A leakage or shunt path will now be formed through the air between the poles -Wand S. Strictly speaking, there will be some leakage in the preceding case of Fig. 48, but with a ferric circuit of comparatively short length, it will have been so small as to be practically negligible. In Fig. 49, however, the reluc- tance of the main circuit between the poles including the air- gaps will be so great as to give rise to a considerable difference of magnetic potential between the poles -Wand 5, so that appre- ciable leakage will occur between these points. The reluctance of the leakage-paths through the air will usually be very com- plex, and difficult to compute, but, in simple geometrical cases, it may be approximately obtained without great difficulty. In this case we may proceed to determine the magnetic circuit first on the assumption that no leakage exists, and second on the assumption of the existence of a known amount of leakage. Assuming that the cores are of soft Norway iron, and that it is required to establish a total flux of 204,000 webers through the circuit, then the flux density in the iron will be 17 kilogausses and its reluctivity 0.0073. The reluctance of the circuit, so far aft it is composed of iron, will be 0.03042 oersted, 1.27 while the reluctance of each air-gap will be X 1 = o. 1058;. or, in all, 0.2016 oersted. The total reluctance of the circuit will, therefore, be 0.23202 oersted, and the M. M. F. required will be 204,000 x 0.23202 =47,330 gilberts = 37,660 ampere- turns; or, with 2,000 turns, 18.83 amperes. The attractive force on the armature will be 620 lbs. as in the previous case. 78. Considering now the effect of leakage, we may assume that the reluctance of the leakage path through the air R 9 , is 0.5 oersted, and that a flux of 108 kilowebers has to be produced through the lower core; the length of mean path in the lower core being 20 cms., and in the upper core 30 cms., it is required to find the M. M. F., which will produce this flux through the lower core. The intensity in the lower core will be J — =9,000 gausses, at which intensity the reluctivity of Norway iron will Digitized by VjOOQ IC AERO-FERRIC MAGNETIC CIRCUITS. 73 be, by Fig. 47, 0.000, 6, so that the reluctance of the lower core 20 will be — x 0.000,6 = 0.001 oersted, and this added to the re- 12 luctance of the two air-gaps, 1. 27 cms. in width, = o. 2016 + 0.001 = o. 2026 oersted. The magnetic difference of potential in this branch of the double circuit will, therefore, be 108,000 x 0.2026 = 21,880 gilberts. This will also be the difference of magnetic potential between the terminals of the leakage path R v and the leakage flux will, therefore, be — = 43,760 webers. The total flux in the main circuit through the upper core will be the sum of the flux in the two branches, or 108,000 + 43,760 = 151,760 webers, making the intensity in the upper core 5 — = 12,647 gausses, at which intensity the reluctivity is o. 001 21, ^o so that the reluctance of the upper core is — X 0.0012 = 12 0.003 oersted. The drop of potential in the upper core will, therefore, be 151,760 x 0.003 = 455 gilberts, and the total difference of potential in the circuit, or the M. M. F., will be 21,880 +455 = 22 >335 gilberts = 17,775 ampere-turns, or 8.89 amperes at 2,000 turns. 79.- It is obvious that the results obtained by the preceding method of calculation cannot be strictly accurate, since no account has been taken of any magnetic leakage except that whicti occurs directly between the poles N and S. Also we have assumed that the flux density remains uniform through- out the lengths of the two cores. When a greater degree of accuracy is desired, corrections may be introduced for the effects of these erroneous assumptions, but the examples illus- trate the general methods by which the magnetic circuits of practical dynamo-electric machines may be computed with fair limits of accuracy. Digitized by VjOOQ IC CHAPTER VII. LAWS OF ELECTRO-DYNAMIC INDUCTION. 80. When a conducting wire is moved through a magnetic flux, there will always be an E. M. F. induced in the wire, unless the motion of the wire coincides with the direction of the flux; or, in other words, unless the wire in its motion does ^ v* FIG. 50. — CONDUCTOR PERPENDICULAR TO UNIFORM MAGNETIC FLUX, AND MOVING AT RIGHT ANGLES TO SAME. not pass through or cut the flux. Thus, if, as iiTFig. 50, a straight wire A B 9 of / cms. length, extending across a uniform flux, be moved, at right angles to the flux, either upwards or downwards, to the position, for example, a d, or a' b\ it will have an E. M. F. induced in it, the direction of which will change with the direction of the motion. 81. A convenient rule for memorizing the direction of the E. M. F. induced in a wire cutting, or moving across, magnetic flux, is known as Fleming's hand rule. Here, as in Fig. 51, the right hand being held, with the thumb, the forefinger and the middle finger extended as shown, the thuwb being so pointed as to indicate the direction of motion, and the/orefinger the direction of the magnetic /lux, then the widdle finger will indi- cate the direction of induced E. M. F. For example, if, as in Digitized by VjOOQ IC LAWS OF ELECTRO-DYNAMIC INDUCTION. 75 Fig. 5°> a WITG be moved vertically downwards from A £ y to a b\ and the thumb be held in that direction, the forefinger pointing in the direction of the flux, the E. M. F. induced in the wire will take the direction a' b\ during the motion, follow- ing the direction of the middle finger. If, however, the wire be moved upwards through the flux, an application of the same FIG. 51. — FLEMING'S HAND RULE. rule will show that the direction of the induced E. M. F., as indicated by the middle finger, is now changed. 82. The induction of electromotive force in a conductor, moving so as to pass through or cut magnetic flux, is called electro-dynamic induction. The value of the E. M. F. induced in a wire by electro-dynamic induction depends, (1.) On«the density of the magnetic flux. (2.) On the velocity of the motion, and (3.) On the length of the wire. This is equivalent to the statement that the E. M. F., in- duced in a given length of wire, depends upon the total amount Digitized by VjOOQ IC 7$ ELECTRO-DYNAMIC MACHINERY. of flux cut by the wire per second in the same direction; or, e = (B / v C. G. S. units of E. M. F. Where (B, is the intensity of the flux in gausses, /, the length of the conductor in cms., v f the velocity of motion in cms.-per- second, and e, the induced electromotive force as measured in C. G. S. units. Since one international volt is equal to x ^\ : ^>>. FIG. 52. — CONDUCTOR OBLIQUE TO UNIFORM MAGNETIC FLUX, AND MOVING AT RIGHT ANGLES TO SAME. 100,000,000 C. G. S. units of E. M. F., the E. M. F. induced in the wire will be <$>lv 100,000,000 volts. 83. The preceding equation assumes that the wire is not only lying at right angles to the flux, but also that it is moved in a direction at right angles to the direction of the flux. If instead of being at right angles to the flux, the wire makes an angle /J, with the perpendicular to the same, as shown in Fig. 52, then the length of the wire has to be considered as the virtual length across the flux, or as its projection on the normal plane, so that the formula becomes, (B/^cos/3 . e =; — volts. 100,000,000 If the motion of the wire, instead of being directed perpendic- ularly to the flux, is such as to make an angle a, with the per- pendicular plane, the effective velocity is that virtually taking igitizedt>yVj< LAWS OF ELECTRO-DYNAMIC INDUCTION. 77 place perpendicular to the flux, or v cos a, as shown in Fig. 53, so that the formula becomes in the most general case, e = tt/coslpcosor voUs 100,000,000 84. It will be seen that in all cases the amount of flux cut through uniformly in one second, gives the value of the E. M. F; FIG. 53.— CONDUCTOR OBLIQUE TO UNIFORM MAGNETIC FLUX, AND MOVING OBLIQUELY TO SAME. induced in the wire, and that the value of the E. M. F. does not -depend upon the amount of flux that has been cut through, or that has to be cut through, but upon the instantaneous rate of ■cutting. The E. M. F. ceases the moment the cutting ceases. 85. If the loop A B C Z>, Fig. 54, be rotated about its .axis O 0' y in the direction of the curved arrows, then, while the side C D, is ascending, the side A B, is descending; con- sequently, the E. M. F. in the side C D> will be oppositely -directed to the E. M. F. in the side A B. Applying Fleming's hand rule to this case, we observe that the directions of these E. M. Fs. are as indicated by the double-headed arrows, and, regarding the conductors CD and A B 9 as forming parts of the complete circuit C D A B 9 it is evident that the E. M. Fs. induced in A B and C Z>, will aid each other, while, if they are permitted to produce a current, the current will flow through the circuit in the same direction. 86. We have seen that no E. M. F. is induced in a wire unless it cuts flux. Consequently, the portions B C and A D> of the circuit which move in the plane of the flux, will con- tribute nothing to the E. M. F. of the circuit. Digitized by VjOOQ IC 78 ELECTRO-DYNAMIC MACHINERY. If the dimensions of the wires forming this loop shown in the figure, are such that C D and A B, having each a length of 12 cms., while A B and B C> are 4 cms. each., the circumfer- ence traced by the wires A B and CD, in their revolution about the axis, will be 3. 1416 X 4 = 12.567 cms.; and, if the rate of rotation be 50 revolutions per second, the speed with which the wires A B and CD, revolve will be 628.3 cms. per second. If the intensity of the magnetic flux B f is uniformly 5 kilogausses, the E. M. F. induced in each of the wires A B FIG. 54. — RECTANGULAR CONDUCTING LOOP ROTATING IN UNIFORM MAGNETIC FLUX. and C D, will be, 5,000 x 12 x 628.32—37,699,200 C. G. S. units of E. M. F., or 0.377 volt. This value of the E. M. F. only exists at the instant when the loop has its plane coincident with the plane of the flux, and the sides cut the flux at right angles. In any other position, the motion of these sides is not at right angles to the flux, so that the E. M. F. is reduced. 87. In order that the E. M. F. induced in a wire may estab- lish a current in it, it is necessary that such wire should form a complete curcuit or loop, as indicated in Fig. 55. When such a conducting loop is moved in a magnetic field, some or all portions of the loop will cut flux, and will thereby contribute a certain E. M. F. around the loop. If the loop moves in its own plane, in a uniform magnetic flux, there will be no resultant E. M. F. generated in it. For example, considering a circular loop, we may compare any two diametrically opposite segments, when it is evident that each member of such a pair cuts through the same amount of flux per second, and will, therefore, gener- ate the same amount of E. M. F., but in directions opposite to each other in the loop. At the same time, it is clear that Digitized by VjOOQ LC LAWS OF ELECTRO-DYNAMIC INDUCTION. 79 the total amount of flux in the loop does not change; for, while the flux is being left by the loop at its receding edge, it is entering the loop at the same rate at its advancing edge, and, since these two quantities of flux are equal, the total amount of flux enclosed by the loop remains constant. 88. The cutting of flux by the edges of a moving loop, there- fore, resolves itself into the more general condition of enclos- ing flux in a loop. The value of the E. M. F. induced around FIG. 55. — CIRCULAR CONDUCTING LOOP PERPENDICULAR TO UNIFORM MAGNETIC FLUX. the loop does not depend upon the actual quantity of flux enclosed, but on the rate at which the enclosure is being made. If, as we have already seen, the loop is so moved that the total flux it encloses undergoes no variation, the amount entering the loop being balanced by the amount leav- ing it, although E. M. Fs. will be induced in those parts of the loop where the flux is entering and where it is leaving, yet these E. M. Fs. being opposite, exactly neutralize each other, and leave no resultant E. M. F. Consequently, the value of the E. M. F. induced at any moment in the loop by any motion, does not depend upon the flux density within the loop, but on the rate of change of flux enclosed. 89. If #, be the total flux in webers contained within a single loop, such as shown at A B C, in Fig. 55, the mean rate at which this flux is changing during any given period of time, will be the quotient of the change in the enclosure, divided by Digitized by VjOOQ IC So ELECTRO-DYNAMIC MACHINERY. that amount of time, so that if $, changes by 20,000 webers in two seconds, the mean rate of change during that time will be 10,000 webers per second, and this will be the E. M. F. in the loop expressed in C. G. S. units. But, during these two seconds of time, the change may not have Been progressing uniformly, in which case only the average E. M. F. can be stated as being equal to the 10,000 C. G. S. units. Where the change is not uniform, the rate at any moment has to be determined by taking an extremely short interval, so that if dt y represents FIG. 5 5 A. — RECTANGULAR CONDUCTING LOOP IN NON-UNIFORM MAGNETIC FLUX. this indefinitely small interval of time, and d$ 9 the correspond- ing change in the flux enclosed during that interval in webers, d$ the rate of change will be — — webers-per-second, and this will be the value of the induced E. M. F. at each instant. 90, If a small square loop of wire A B C Z>, one cm. in length of edge, placed at right angles to the flux as shown in Fig. 55A, contains a total quantity of flux amounting to 10,000 webers, the mean flux density at the position occupied by the square, will be 10,000 gausses. If now, the loop be moved uniformly upward in its own plane to the position a bed, so as to accomplish the journey in the — th part of a second, and if the flux enclosed by the loop at the position a bed, be 1,000 webers, then 9,000 webers will have escaped from the loop during the motion. Assuming that the distribution of flux density in the field was such that the emission took Digitized by VjOOQ LC LAWS OF ELECTRO-DYNAMIC INDUCTION. 81 place uniformly, the E. M. F. in the loop, during the passage, will have been, A $ 0,000 -jrr = —z = 900,000 C. G. S. units = 0.009 vo ^« 91. If, however, the rate of emptying, during the motion, were not uniform, 0.009 volt would be the average E. M. F., and not the E. M. F. sustained during the interval; or, in other words, the instantaneous value of the E. M. F. in the loop would vary at different portions of this short interval of time, or at corresponding different positions during the jour- ney ; but, in all cases, the time integral of the E. M. F. will be equal to the change in $ ; thus, the change in $, is, in this case, 9,000 webers. If the motion is made in — th of a 100 second, the E. M. F., will be 900,000 C. G. S. units of E. M. F., which, multiplied by the time (0.01 second), gives 9,000 webers. If, however, the motion were uniformly made in half a second, the E. M. F. would have been 18,000 C. G. S. units, which, multiplied by the time, would give as before 9,000 webers; and under whatever circumstances of velocity the change were made, the sum of the products of the instantaneous values of E. M. F. multiplied into the intervals of time during which they existed, would give the total change in flux of 9,000 webers. Or in symbols, c . d$ Since e = --=- - at fedt- 4 The first equation simply expresses that the E. M. F., t, is the instantaneous rate of change in the flux enclosed, and the second equation shows that the difference in the enclosure between any two conditions of the loop is the time integral of the E. M. F., which has been induced in the loop during the change, assuming of course, that the change continues in the same direction ; i. *., that the flux through the loop has con- tinually increased or decreased. 92. If a circuit contains more than one loop, as, for example, when composed in whole, or in part, of a coil, the turns of which are all in series, the E. M. F. induced in any one turn Digitized by VjOOQ IC 8a ELECTRO-DYNAMIC MACHINERY. or loop of the coil, may be regarded as being established inde- pendently of all the other loops, so that the total E. M. F. in the circuit will be the sum of all the separate £. M. Fs. exist- ing at any instant in the loops, and may, therefore, be regarded as the instantaneous rate of change in the flux linked with the entire circuit. A coil, therefore, may be regarded as a device for increasing the amount of flux magnetically linked with an electric circuit, so that by increasing the number of loops of conductor in the circuit, the value of the induced E. M. F. corresponding to any change in the flux, is proportionally increased, and if the coil or system of loops forming the cir- c FIG. 56.— CLOSED CIRCULAR HELIX LINKED WITH A LOOP OF WIRE. cuit, contains in the aggregate $ webers of flux linked with it, taking each turn separately and summing the enclosures, then the time integral of E. M. F. in the circuit will be the total change in $, and this will be true, whether the loop is chang- ing its position, or whether the flux is changing in intensity or in direction. 93. It is evident from the preceding, that there are two different standpoints from which we may regard the produc- tion of electromotive force in a conducting circuit by electro- dynamic induction ; namely, that of cutting magnetic flux, and that of enclosing magnetic flux. These two conceptions are equivalent, being but different ways of regarding the same phenomenon. The amount of flux enclosed by a loop can only vary by the flux being cut at the entering edge or edges at a different rate to that at the receding edge; or, in mathe- matical language, the surface integral of enclosing is equal to Digitized by VjOOQ IC LAWS OF ELECTRO-DYNAMIC INDUCTION. 83 the line integral of cutting, taken once round the loop. This statement is equally true whether the flux is at rest and the conductor moving, or the conductor at rest and the flux mov- ing, or whether both conductor and flux are in relative motion. 94. Cases of electro-dynamic induction may occur where the equivalence of cutting and enclosing magnetic flux apparently fails. On closer examination, however, the equivalence will be manifest. For example, in Fig. 56, let A B C D be a wooden anchor ring uniformly wound with wire, as shown in Fig. 44, and a b c d 9 a circular loop of conductor linked with the ring. >>* FIG. 57. — SQUARE CONDUCTING LOOP ROTATED IN UNIFORM FLUX. FIRST POSITION. It has been experimentally observed that when a powerful cur- rent is sent through the winding of the anchor ring, no appreci- able magnetic flux is to be found at any point outside the ring, although within the core of the ring a powerful magnetic flux is developed. Nevertheless, both at the moment of applying and at the moment of removing the exciting current through the winding of the ring, an E. M. F. is induced in the loop abed, whose time integral in C. G. S. units, is the total number of webers of change of flux in the ring core. It might appear at first sight that this E. M. F. so induced in the loop cannot be due to the cutting of flux by the loop, but must be due to simple threading or enclosing of flux. It is clear, how- ever, that the mere act of enclosure will not account for the induction of the E. M. F., since the passage of flux through the centre of the loop cannot produce E. M. F. in the loop itself, unless activity is transmitted from the centre of the loop Digitized by VjOOQ IC 84 ELECTRO-DYNAMIC MACHINERY. to its periphery. In other words, action at a distance, with- out intervening mechanism of propagation, is believed to be impossible. Could we see the action which occurs when the current first passes through the ring-winding, we should observe flux apparently issuing from all parts of the ring and passing into surrounding space, at a definite speed. The loop abed, would receive the impact of flux from the adjacent portions of the ring before receiving that from the more distant parts of the ring, and, in this sense, would actually be cut by the flux. As soon as the flux has become established, and the current in FIG. 58. — SQUARE CONDUCTING LOOP ROTATED IN UNIFORM FLUX. SECOND POSITION. the winding steady, it is found that the flux from any particu- lar portion of the ring is equal and opposite to that from the remainder of the ring, and is, therefore, cancelled or annulled at all points except within the ring core. It is evident, there- fore, that we may regard the E. M. F induced in the loop a b c d as due either to the cutting of the boundary by flux, or to the enclosure of flux. 95. Let us consider the case of a square conducting loop A B C J?, Fig. 57, having its plane parallel with the uniform magnetic flux shown by the dotted arrows. If this loop be rotated about the axis O 0\ which is- at right angles to the magnetic flux, and symmetrically placed with regard to the loop, so that A Z>, descends, and B C, ascends, these sides, which cut flux during the rotation, will have E. M. Fs. gene- rated in them, in accordance with Fleming's hand rule already Digitized by VjOOQ IC LAWS OF ELECTRO-DYNAMfcJkmiCTibN. 85 described in Par. 81, and in the direction shown «by the double arrows. The sides A £ and D C 9 which do not cut flux during the motion, will .add nothing to the E. M. F. generated. The figure shows that while the sides A D and C£, have oppo- sitely directed E. M. Fs., yet regarding the entire loop as a conducting circuit, these E. M. Fs. tend to produce a current which circulates in the same direction. 96. As already pointed out, the value of the E. M. F. gene- rated in the sides A D and C B> of the loop, by the cutting of the flux, will depend upon the rate of filling and emptying the FIG. 59. — SQUARE CONDUCTING LOOP ROTATED IN UNIFORM FLUX. THIRD POSITION. loop with flux, and it is evident that this rate is at a maximum when the loop is empty; *.'*., in the position it occupies in Fig. 57, when the plane of the loop coincides with the direc- tion of the flux, and the motion of its sides is at right angles thereto; for, when the loop reaches the position shown in Fig. 58, namely, when it is full of flux; or, when its plane is as right angles to the flux, then at that instant the rotation of the loop neither adds to nor diminishes, the amount of flux enclosed, so that the E. M. F. in the loop is zero. 97. Continuing the rotation of the loop in the same direc- tion, the E. M. F. generated will increase from this position until the position shown in Fig. 59 is reached, where the plane of the loop is again coincident with the plane of the flux, but in which the side A D, has moved through 180 , or one-half a revolution from the position shown in Fig. 57, and the direc- tions of E. M. Fs. in the wire, as shown, will be changed so far Digitized by VjOOQ IC 86 ELECTRO-DYNAMIC MACHINERY. as the wire is concerned, being now from A to Z>, instead of from D to A, in the conducting branch A D; and from C to B, instead of from B to C, in the conducting branch B C. The direction of £. M. F. around the loop, will, therefore, be FIG. 60. — SQUARE CONDUCTING LOOP ROTATED IN UNIFORM FLUX. FOURTH POSITION. reversed. Consequently, the loop A B C D % during its first half revolution as shown in Figs. 57 to 59, has an E. M. F. in it in the same direction; and, during the remaining half-revolu- tion, has its E. M. F. in the reverse direction, as shown. FIG. 6l. — FLUX OBLIQUE TO PLANE OF ROTATING LOOP. 98. The value of the E. M. F. generated in a loop, during its rotation, depends upon the flux density, on the area of the loop, and on the rate of rotation. Assuming the side of the loop C D y to occupy the position shown in Fig. 61, making an angle a, with the direction H K y of the flux, then the E. M. F. generated in the loop at this instant is the rate at which flux is being admitted into the loop. If /cms., be the length of the side of the loop or the length of A £>, in Fig. 57, the amount of flux embraced at this instant will bt I (S> X 2 D K. During the next succeeding small interval Digitized by VjOOQ LC LAWS OF ELECTRO-DYNAMIC INDUCTION. »7 of time dt, if the angular velocity of the loop, co radians per second, carries it to the position C'D\ the amount of flux admitted during that time will be / ' xcos or, and D D\ will be —codt 2 cms. in length, since the radius 01? = —; consequently, the flux admitted into the loop during this brief interval of time dt % will be d $ =z 2 / x — (Bg> cos a dt, or P ($> co cos a dt = co cos a dt so that Thus, at the instant of time in which the loop has reached the d' d r i -T- =

5°o webers. This flux, divided by the area through which it passes, *.u • ^ • *. 5.500,000 gives the intensity, or — — - — = 1,000 gausses. 5>5°° (2.) The magnetic intensity is, as we have seen (Par. 53), numerically equal to the drop of magnetic potential in air, or other non-magnetic material, per centimetre, so that the drop 8 DEGREE* OF ANGULAR \| DEVIATION FROM I jfl^J VlftTIOALRWUaO* ] FIG. 69. — DIAGRAM OF MAGNETIC INTENSITY IN AIR-GAP. of potential being here 1,000 gilberts in 1 cm. of distance in air, the intensity must be 1,000 gausses. Representing the in- tensity graphically, as shown in Fig. 69, it will be seen that the intensity is uniform from c to e 9 Fig. 68, and then descends rapidly to zero at B, where it changes sign and becomes negatively directed, and is then uniform from / to d, falling again to zero at A. The flux direction, therefore, changes sign twice in each revolution. 103. If a wire A B, be wound as a loop around the armature, it will, when the armature revolves, cut this flux at right angles, and will, therefore, have induced in it an E. M. F. which must be of the same type graphically as the curve in Fig. 69. Thus, if the surface of the armature moves at a rate of 50 cms. per second, the E. M. F. induced in the loop will be 2 v I (R, the factor 2 being required, since both sides of the loop are cutting flux, one at A, and the other at B; or, 2 X 50 x too x 1,000 = 10,000,000 C. G. S. units =0.1 volt. Digitized by VjOOQ LC INDUCTION IN DYNAMO ARMATURES. 93 ■except at the moment when the wires emerge from beneath the pole pieces. This curve is represented in Fig. 70, where the distance O F, represents the time of one complete revolu- tion of the armature, and the elevation of A, corresponds to 0.1 volt. If the armature be set revolving at twice this speed, the time occupied in a revolution will be halved, but the E. M. F. being proportional to the rate of cutting flux, will d £ fig. 70. — diagram of induced e. m. f. in armature turn. l>e doubled, as represented in Fig. 71, where the E. M. F. is alternately 0.2 volt in each direction. By the aid of a suitably adjusted commutator, the E. M. F. instead of changing sign, can be kept unidirectional in an external cir- cuit, following the curve ab c k l/g hj. 104. We may regard the E. M. F. of the loop as being in- duced either by the cutting of the flux by the wire at the arma- ria. FIG. 71. — DIAGRAM OF INDUCED E. M. F. IN ARMATURE TURN AT DOUBLED SPEED OF ROTATION. ture surface, or by the enclosure of the flux by the loop. The flux enclosed by the loop is represented by Fig. 72, where at the initial position at A £, the loop encloses 5,500,000 webers. As the armature is rotated counter-clockwise, so that A, is -carried toward N, the flux enclosed by the loop diminishes, until, when it reaches the horizontal position, the flux through the loop is zero. As the rotation continues, the flux re-enters the loop in the opposite direction, and becomes 5.5 mega- Digitized by VjOOQ IC 94 ELECTRO DYNAMIC MACHINERY. webers at a position 180 distant from the initial position A B. The rate of change of flux enclosed, or the gradient of the curve, shown in Fig. 72, is uniform, since the curve is uni- formly steep, except near the position of maximum flux, where the gradient is considerably reduced, and the E. M. F. cor- respondingly reduced as already observed in Figs. 70 and 71. FIG. 72. — REPRESENTING DIAGRAM OF FLUX ENCLOSED BY LOOP OF ARMATURE. 105. When, however, the wire instead of being on the sur- face of the armature is buried in a groove in the iron, as in a toothed-core armature (Par. 22), and as shown in Fig. 73, it is often -mere convenient, for purposes of calculation, to con- sider the E. M. F. as dueto^enclosing, rather than to cutting flux. The following rule, will, therefore, be . of assistance in FIG. 73. — ARMATURE LOOP ROTATING IN BIPOLAR FIELD. determining the direction of the E. M. F. induced in a loop. Bearing in mind the fact that a watch dial is visible, to an ob- server who holds it facing him, by the light which proceeds in straight lines from the watch to his eye, then the direction of the E. M. F. induced in the loop, regarded as the outline of the watch face, can be remembered by the following rule. Digitized by VjOOQ IC INDUCTION IN DYNAMO ARMATURES. 95 The E. M> F. induced in the loop has the same direction as the motion of the hands of the watch, when the flux entering the loop has the same direction as theMght. 106. Flux entering the loop in the opposite direction, or from the observer, will induce an E. M. F. in the opposite direction to the hands of the watch, that is, counter-clockwise. Emptying a loop of flux produces in it an E. M. F. in the opposite direction to that produced by filling it FIG. 74. — DIAGRAMS OF E. H. F. 107. Fig. 68, shows a single loop of wire wound upon a drum armature, which by its rotation in the flux, has an E. M. F. induced in it of the same type as is graphically repre- sented in the curve of Fig. 69. Supposing that the speed of revolution is such as to produce an E. M. F. of say one volt, in this conducting loop, during its passage beneath the pole faces, then if two turns of wire be wound on the armature at xight angles, as shown at A B and CD, Fig. 75, they will each generate E. M. F. of the same value, in their proper order, as they pass through the flux, and if the E. M. F. from A B, is represented by the curve of a b c d e f g, of Fig. 74 A, and the E. M. F. in the loop CD, be represented simultaneously by the Digitized by VjOOQ IC 9 6 ELECTRO-DYNAMIC MACHINERY. curve of hijklmn o, of Fig. 74 B, then, by properly adding and co-directing the . E. M. Fs. so produced, by the aid of a suitable commutator, we obtain an E. M. F. of two volts, as shown in Fig. 75, C, by the curve pqrstuvwxyzz' z". Moreover, while the E. M. F. produced from one wire alone FIG. 75. — DRUM ARMATURE WOUND WITH TWO TURNS OF WIRE AT RIGHT ANGLES TO EACH OTHER. fluctuates between o and 1 volt, four times per revolution, the E. M. F. produced by the combination fluctuates between 1 and 2 volts-, eight times per revolution. 108. If now, instead of two loops being wound on the arma- ture, there are six loops, as shown in Fig. 76, the E. M. F. 9 etc., touches the zero line at this point B. Again at the point q, on the flux curve, if the change of flux were to continue for one second uniformly at this rate, we should follow the dotted line or tangent q q\ which reaches the ordinate —400, or 500 below q\ so that the rate of change at the point q, on the curve is 500 kiiowebers, represented by the point Q, on the E. M. F. curve at that ordinate. Con- tinuing in this way we trace the E. M. F. curve O A B C D y etc., showing that an alternating E. M. F. is produced in the armature, varying between +7.7 and —7.7 volts. At the rate of rotation assumed; namely, ij4 revolutions per second, there will be three alternations of E. M. F. per second, or twice the number of revolutions in that time. 119. Having now examined the means for determining the value of the E. M. F. developed in the armature, we will con- sider the effect of the commutator. It will be seen by refer- ence to Figs. 85 to 88, the brushes B 9 B\ resting on the segments of the two-part commutator, that the direction of E. M. F. from the armature toward the external circuit is reversed at the moment when the core passes the position of maximum contained flux, as indicated by the change in the direction of the dotted loops C £>' E' and L M' N', relatively to the horizontal line. The E. M. F. generated by the armature as produced at the brushes B, B\ will be represented by the pulsating E. M. F., O A B C D' E F G H I K L AT N\ It is evident that had we selected a higher rate of rotation, the E. M. F. of the machine would have been correspondingly increased. Digitized by VjOOQ IC MAGNETO GENERATORS. 109 120. The preceding considerations can only determine the value of the £. M. F. at the brushes, while the external circuit is open. As soon as the circuit of the armature is closed, the E. M. F. at the brushes is reduced, for the following reasons; viz., (1.) The current in the armature always produces an M. M. F., counter, or opposite to the M. M. F. of the field magnet, and, therefore, diminishes the flux through the magnetic circuit, thus causing a corresponding diminution in the value of the E. M. F. produced. Indeed, this opposing M. M. F. may, under certain circumstances, assume a magnitude sufficient to neutralize and destroy the permanent M. M. F. in the field magnets. This is one of the reasons why magneto generators are not employed on a large scale in practice. (2.) The current through the armature produces in the resistance of the armature, a drop in the E. M. F. If, for example, the current through the armature at any instant be one ampere, and the resistance of the armature be 10 ohms, then in accordance with Ohm's law, the drop of E. M. F. pro- duced in the armature, will be 1 X 10 = 10 volts. (3.) The current through the armature not being steady, but pulsating, the variations in current strength will induce E. M. Fs. in the coil opposed to the change and, therefore, reducing the effective E. M. F. Digitized by VjOOQ IC CHAPTER X. POLE ARMATURES. 121. The form of armature, which stands next in order of complexity to the shuttle-wound armature last described, is the radial ox pole armature, represented in Figs. .91 and 92. Here the armature coils c, c, are wrapped, usually by hand, around radially extending laminated pole-pieces, formed from sheet iron punchings laid side by side. This type of machine is rarely found in continuous current generators, but is some- times adopted in very small motors. The winding of such an armature is carried out as represented in Fig. 93, where the pole-pieces are shown at P P, and P' P\ Starting the wind- ing at the point M, the coil A 9 is wound from A to B f as shown; the coil C, is then wound from B n through Cto D; the coil E, from Z>, through E to F; the coil G, from E f through G to H; the coil /, from H> through / to K; the coil Z, from K y through L to M, finally connecting the last end of the coil M, to the first end of the coil A, thus making the closed-coil winding shown in the fi-gure. The connections of this winding to the six-part commutator will be seen from an inspection of the figure. The points M y £, £>, F, Zf and K> are branches connected to the separate insulating segments of the commu- tator, brushes being provided in the position shown on a line connecting the centres of the pole-pieces. This commutator is shown in cross-section at P, Fig. 92. It will be seen that, owing to the conical boundaries of each armature coil, the winding is difficult to arrange. This type of generator is always operated by an electro-magnetic field. 122. Since the dimensions of machines with pole or radial armatures are always small, the reluctance of the circuit is practically wholly resident in the air spaces between the poles and armature projections, provided care be taken that the iron in the armature is not worked at an intensity above 10 kilo* Digitized by VjOOQ LC POLE ARMATURES. Ill gausses, or above 7 kilogausses in the field magnet, if the latter be of cast iron. If S 9 be the area of the polar face of a radial armature projection in square centimetres, and d f be the clear- d ance or entrefer in cms., then -=- will be the reluctance of the entrefer over each armature projection. Since there are four FIG. 91. — POLE ARMATURE AT RIGHT ANGLES TO AXIS. such air-gaps in multiple-series the total reluctance of the cir- cuit provided in the case represented, by Fig. 91, will be FIG. 92. — SECTION OF POLE ARMATURE THROUGH AXIS. d -~- oersteds, assuming that the reluctance existing in the iron is neglected. 123. The distribution of the flux through the armature is diagrammatically represented in Fig. 95. If the cross-section of each armature core be s, square centimeters, then at no time will there be less than two radial projections carrying the total flux, and if 10 kilogausses be the limit permitted by the Digitized by VjOOQ LC 112 ELECTRO-DYNAMIC MACHINERY. reluctance of the air-gap, the total flux to be forced through the armature will be 2 s x 10,000 = 20,000 s f webers. The M. M. F. necessary on the field magnets will be 20,000 s x ~«- gil- berts. For example, if s = 1.3 sq. cms., d = o. 2 cm., s = 10 sq. cms., the M. M. F. required will be 26,000 x 0.02 = 520 gil- berts = 416 ampere-turns, and this must be the total excitation included on the limbs of the electro-magnet. 124. In order to determine the amount of flux passing through a single projection, let the armature be considered as slowly rotated counter-clockwise. Starting with the core 1, FIG. 93. — DIAGRAM SHOWING CONNECTIONS OF COIL WITH COMMUTATOR. Fig. 95, the magnetic flux passing through it will be found by dividing half the M. M. F. by the reluctance of the air-gap over its face, or — = 13,000 webers. As it moves counter-clock- 0.2 10 wise towards 2, no appreciable change is effected in the amount of flux it carries, until the advancing edge of 2 emerges from beneath the polar face N r The flux through 1, rapidly dimin- ishes until before 1 becomes halfway between the pole faces JV 2 and 5„ it is entirely deprived of flux. When the position 3 is reached, the flux re-enters the coil of 1, but in the opposite direction, and when it passes position 3, the total maximum flux of 13 kilowebers is in the reverse direction. The curve, Fig. 94, commences at 13 kilowebers in the position corresponding to 1, Fig. 91, falls steadily from B to C, and, after a short pause, from C to Z>, where the coil lies midway between the poles, falls again from D to E, until the flux is 13 kilowebers negative, corresponding to the position 4. Con- Digitized by VjOOQ LC POLE ARMATURES. "3 tinning at this value to F, it rises to G, corresponding to the position 5, and then pauses at the zero line, in the gap between v the poles, rising finally to /, corresponding to the original position i, at K. 125. The £. M. F. established in any turn of the coil is found by ascertaining, from the speed of rotation, the rapidity with which the flux, threading through the coil, changes in value. If, for example, the armature be driven at a speed of 1,500 FIG. 94. — DIAGRAM SHOWING FLUX PASSING THROUGH ONE ARMATURE PRO- JECTION DURING A COMPLETE REVOLUTION. revolutions per minute, or 25 revolutions per second, cor- responding to the time of 0.04 second per revolution, the E. M. F. will evidently be zero at the positions represented by the straight line A B, C Z>, E F f G H 9 and / K of Fig. 94, since here, the rate of change in the flux is practically zero, and the E. M. F. will be nearly uniform during the periods repre- sented by B C, D E, F G, and H /, since the rate of change is nearly uniform in one direction or the other during those periods. As shown in Fig. 97, the E. M. F. in the single turn on the projection commencing at the position 1, is zero from o to b. From b, through V to r, the flux diminishing at the rate of 13,000 webers in 0.00433 second, and, therefore, at the rate of 3,000,000 webers (3 megawebers) per second, and since 100 megawebers per second correspond to an E. M. F. of one volt, the E. M. F. in a single turn is —0.03 volt. Assuming 10 turns of wire on each armature projection, the total E. M. F. will be —0.3 volt at this period, and the ordinate bb 9 represents Digitized by VjOOQ LC "4 ELECTRO-DYNAMIC MACHINERY. —0.3 volt in Fig. 97. At c'd 9 corresponding to the position CD, Fig. 94, the E. M. F. is zero, falling again to —0.3 volt from d to e\ corresponding to a change in flux from D to E, Fig. 94. After 0.02 second has elapsed, the E. M. F. re- verses in direction and becomes positive, tracing the curve ff' gg' hh'jf k. By the aid of the commutator, the E. M. Fs. in the coils, as soon as they change their direction, are reversed relatively FIGS. 95 AND 96. — DISTRIBUTION OF FLUX AND E. M. F. AT POSITION SHOWN. to the external circuit, and, therefore, preserve their direction externally, as can be seen by examination of Fig. 93. 126. We have thus far traced the E. M. F. as developed in a single polar projection, and so resulting from the variation of flux passing through it. During the time that the E. M. F. is being generated in this coil, a similar E. M. F. is being gener- rated in the other coils, displaced, however, in time, by por- tions of a revolution. As shown in Fig. 96, the six coils on the armature have E. M. Fs. developed in them, being con- nected with the external circuit through the brushes in two parallel series, each of 3 series-connected coils. Each coil is, therefore, acting in its circuit for one half of a revolution before it is transferred to the opposite side, and while Fig. 97 represents the E. M. F. generated in any half revolution of one coil, we have to consider the E. M. Fs. coincidently being generated in its next neighbor on either side. This is shown in Fig. 98, where the E. M. F. of all three coils is de- Digitized by VjOOQ LC POLE ARMATURES, "5 veloped independently on parallel lines one above the other, each E. M. F. being a repetition of that in Fig. 98, but dis- placed the |th of a complete revolution. Fig. 99 represents M •J t'r-A *-/ e'd •' , / pc #-; FIG. 97. tt'K j' * s FIG. 98. FIG. 99. FIGS. 97, 98, AND 99. — E. M. F. WAVES GENERATED IN POLE ARMATURE. the effects of combining or summing these three separately generated E. M. Fs. in the same circuit, and it will be seen that the E. M. F. pulsates between 0.2 and 0.6 volt. 127. If the resistance of the wire on each coil be r ohms, then the resistance of the three coils on each side of the arma- ture will be 3 r, and the resistance of these two sides in parallel will, except at changes of segments, be 1.5 r, so that, neglect- ing the resistance of the brushes and brush contacts, the resist- ance of the armature will be 1.5 r ohms. Digitized by VjOOQ IC Ii6 ELECTRO-DYNAMIC MACHINERY. The current strength which should be maintained by the generator, when on short circuit, would, therefore, reach 0.6 — — amperes, but in reality, the current will not reach this amount, owing, among other things, to the effect of self-in- duction in the armature, which, under load, tends to check the pulsations, and, consequently, renders them more nearly uniform, thus reducing the mean E. M. F. Digitized by VjOOQ LC CHAPTER XL GRAMME-RING ARMATURES. 128. The armature of the dynamo-electric machine which comes next in order of complexity, is that devised by Gramme, and now known generally as the Gramme-ring arma- ture. This armature, as its name indicates, belongs to the type of ring armatures, and consists essentially of a ring-shaped laminated iron core wound with coils of insulated wire. In FIG. IOO. — DIAGRAM OF GRAMME-RING ARMATURE IN BIPOLAR FIELD, TWENTY-FOUR SEPARATE TURNS. the Gramme-ring armature shown in Fig. 100, the core is a simple ring of iron, wound with 24 separate turns of wire, placed so as to be able to revolve about its axis in the bipolar field N, S. Considering the ring to be first at rest, the turns 6, 7, 8, 18, 19 and 20 are represented as being linked with the total flux passing through the cross-section of the ring. If the total flux entering the armature at the north pole and leaving at the south pole, that is, passing from N to S, be two mega- webers, then one megaweber passes through the upper half of the ring, and one megaweber through the lower half. The loops 5, 9, 17 and 21 are diagrammaticaliy represented as hav- ing 900 kilowebers passing through them. The loops 4, 10, 16 and 22 carry 700 kilowebers ; 3, 11, 15 and 23 carry 500 kilowebers ; a, 12, 14 and 24, 300 kilowebers ; while 1 and 13 carry no flux. Digitized by VjOOQ IC Il8 ELECTRO-DYNAMIC MACHINERY. 129. Suppose now, the ring be given a uniform rotation of one revolution per second, in the direction of the large arrows. It is evident, that at any instant there is no change in the amount of flux linked with the turns occupying the positions 6, 7, 8, 18, 19 and 20 ; so that, although these contain a maxi- mum amount of flux, they will have no E. M. F. generated in them. Loops 5 and 9, however, are in a position at which the flux they contain is changing ; that is to say, the amount of flux that is passing through them at each instant has neither reached a maximum nor minimum ; and the same is true with regard to the loops 17 and 21. In 5, the flux is increasing, and in 9, it is decreasing ; consequently, the E. M. F. in 5 is directed oppositely to that in 9, and, according to rule, is in- dicated by the curved arrows (Par. 105); for, if coil 5 be regarded by an observer facing it from S, the flux, as the ring moves on, will thread the loop in the opposite direction* to that of light coming from the face of the loop, considered as a watch dial, to the observer, and the E. M. F. generated in the loop will be directed counter-clockwise, while the E. M. F. in the loop 9 must have the opposite direction. Moreover, simi- lar reasoning will show that all the coils to the left of the line B B\ that have E. M. Fs. generated in them, will have these E. M. Fs. similarly directed ; i. e. , outwards, as shown, while all on the left-hand side of the line, will have the E. M. Fs. also similarly directed, but inwards. Loops 1 and 13, which lie parallel to the direction of the flux, will, in the position shown, have no flux threading through them, but during rota- tion, the rate of change of flux linked with them is a maxi- mum ; consequently, the E. M. F. induced in them is a maximum. 130. Instead of conceiving separate conducting loops to be wound on the surface of the armature, as shown in Fig. 100, let us suppose a continuous coil is wound on the surface of the armature as shown in Fig. 101, the first and last ends of the coils being connected together so as to make the winding con- tinuous; then it is evident that the E. M. Fs. so acting being similarly directed on each side of the vertical line B B\ might be made to produce continuously an E. M. F. in the conduct- ing wire. Moreover, if two wires, or collecting brushes, were Digitized by VjOOQ LC GRAMME-RING ARMATURES. "9 employed in the positions B, B\ the E. M. Fs. from the two halves of the ring would unite at the brushes B, B 1 . Such a condition finds its analogue in the E. M. Fs. pro- duced by two series-connected voltaic batteries connected as shown in Fig. 102, with their positive poles united at B f and their negative poles united at B'. The figure shows two bat- teries each of 9 cells connected in series. Here, as indicated, all the cells have equal E. M. F. This condition of affairs need not, however, exist in the Gramme-ring analogue, since the only requirement is that the sum of all the E. M. Fs. FIG. IOI. — DIAGRAM OF GRAMME-RING ARMATURE IN BIPOLAR FIELD, TWENTY;FOUR SEPARATE TURNS. generated in the coils on the right-hand side be equal to the sum of those on the left-hand side. In point of fact, as already observed, the E. M. Fs. are not the same in each of the coils, those at 1 and 13 having a maximum E. M. F., and those at 7 and 19 having zero E. M. F. Since these oppositely directed E. M. Fs. balance each other, no current will be pro- duced in the armature unless an external circuit be provided, by joining the brushes B, B'. 131. Figure 100 shows no difference between the amount of flux threaded through the coils 6, 7 and 8 ; or 18, 19 and 30, and, consequently, according to theory, a total absence of induced E. M. F. in these coils. In practice, however, owing to leakage (Par. 77) and other causes, no coil is entirely free from having E. M. F. generated in it. Moreover, the difference in the E. M. F. generated in coils 13, 12, 11 and 10, is not as great as might be inferred from their angular position on the armature, owing to the fact that Digitized by VjOOQ IC 120 ELECTRO-DYNAMIC MACHINERY. (Par. ioo) the flux enters the armature core nearly uniformly- all around its surface. In order to determine the total E. M. F. generated in such an armature as is represented in Fig. 101, it is first necessary to determine the E. M. F. generated in a single turn. Let us consider a turn starting from the position 7, and therefore, generating no E. M. F., being carried by the uniform rotation of the armature in the direction of the arrows to the position 19, in a time / seconds. During this time the flux threading through it changes from — webers in one direction, to — • 2 2 wdbers in the opposite direction, and, therefore, the change in flux linkage will be

a bipolar armature will be — ohms, since two halves of the winding are- in parallel; consequently, the resistance of the armature will depend upon the shape of its cross-section, since on this depends the length of each turn of conductor. A, B, and C y Fig. 109, represent the cross-sections of three different armature cores having the same area. Calling the length of one turn around A, unity, the length of a turn around £, will be 7 per cent, greater, and around C, 40 per cent, greater. Consequently, two armatures having respectively the cross- sections of A and C, and wound with the same size and number of turns of conductor, would have the same E. M. F., if driven at the same speed, when traversed Jby the same flux, but the armature C f would have 40 per cent, more resistance than the armature A, and its electrical capability would be about 30 per cent, less, ( — }. It is, therefore, desirable in * 1.4 designing a Gramme-ring armature, to retain a nearly square cross-section. On the other hand, the section shown at C, offers for a given polar arc, a larger surface, and, con- sequently, a lower reluctance to the passage of the flux in the air-gap or entrefer, than in the case of the section A, so that it may be sometimes desirable to employ an armature of the type B y in order to reduce the air-gap reluctance, and, at the same time, not greatly to increase the length of winding. It has been aptly remarked that a dynamo is a combination of compromises, since no single desideratum in its design can be completely realized. Digitized by VjOOQ IC CHAPTER XII. CALCULATION OF THE WINDINGS OF A GRAMME-RING DYNAMO. 137. In order to show the application of the foregoing principles tp the calculation of the E. M. F. produced in an armature of the Gramme type, we will take the case of a FIG. IIO. — GRAMME TYPE ARC MACHINE. bipolar Gramme-wound armature from dimensions given by Messrs. Owen and Skinner in a paper read before the American Institute of Electrical Engineers, May 16, 1894, to which paper the reader is referred for fuller particulars of construction and results. Fig. no, reproduced from the paper referred to, shows a vertical and a longitudinal cross-section of the machine, which is a bipolar, constant-current, Gramme-wound generator, of the Wood type, intended for the supply of any number of arc Digitized by VjOOQ IC WINDINGS OF A GRAMME-RING DYNAMO. 129 lamps in series up to 25, and, therefore, capable of supplying a total E. M. F. of approximately 1,200 volts at terminals, with a current strength of approximately, 10 amperes and an external activity of about 12 KW. This machine, when complete, closely resembles the gener- ator shown in Fig. in. Referring to Fig. no, the field magnet frame of cast iron is shown at Af, Af, Af, Af, the field coils being wound on spools and filling the spaces indicated. The shaft of the machine is supported in bearings B, B, and FIG. III.— GRAMME TYPE ARC MACHINE. space is left on the shaft for a commutator, at C, and a driv- ing pulley at P". The bipolar field poles, produced by the M. M. F. of the magnet coils Af, Af, Af, Af, are shown at P P, P' P'. The Gramme-wound ring armature is shown at AAA. The dimensions of the machine are indicated in inches on the figures. 138. The field winding consists of 100 lbs. of No. 10 B. & S. gauge, single cotton-covered copper wire, the total resistance of the four coils in series being 15.75 ohms hot. The arma- ture core is composed of soft charcoal iron wire of the cross- Digitized by LfOOQ IC 130 ELECTRO-DYNAMIC MACHINERY. section shown. It is wound in 15 layers of No. 10 B. & S. gauge, and contains about 9,450 wires, each having a cross- section of 0.00817 square inch, or a total cross-section of 77.2 square inches = 498.1 sq. cms. The armature is wound in 100 sections of No. 14 B. & S. gauge, double cotton- covered copper wire, in 57 turns each, or 5; 700 turns, making a total of 115 lbs. of wire, with a total resistance of 28.8 ohms hot, but which, being connected in two parallel halves, as repre- sented in the figure, has a joint resistance between brushes of 7.2 ohms. Assuming 10 amperes to flow through the machine, the drop in the armature will be 72 volts, and the drop in the field magnets 157.5 volts, making the total drop in the machine 229.5 volts. When, therefore, the pressure at the machine terminals is 1,200 volts, the E. M. F. generated by the machine is practically 1,430 volts, or 1,430 X io 8 = 1.430 X io 11 C. G. S. units of E. M. F. 139. The formula for determining the E. M. F. generated by a bipolar armature is JE = $nw C G. S. units (Par. 132). zp Consequently, # = ■ n w The speed of this generator is stated to be 1,000 revolutions per minute, or 16.67 revolutions per second, and w, is 5,700, therefore, $ = 'l 43 X IO = 1.505 x io 6 . The total 16.67 x 5>7°° flux through the armature is, therefore, 1.5 megawebers. 140. Assuming that the M. M. F. required for this machine were not known, it could be calculated in the following way: We first determine the flux density in the various parts of the circuit, and from that the reluctivity and reluctance of the various portions. The cross-section of the armature core, as already stated, is 498 sq. cms. and if the flux goes through each side or cross-section of the armature, the intensity in the armature o. 7«; X 10" _, , is, therefore, — — — - = 15,060 gausses. The arc covered 495 by each pole-piece is, approximately, 55 cms., and the effective breadth 6.5" = 16.5 cms., so that the area of the polar surface WINDINGS OF A GRAMME-RING DYNAMO. 131 is, approximately, 55 x 16.5 = 907.5 sq. cms. The total flux passes through this surface, and the mean intensity in the . 1.5 x io* air-gap is — - = 16.58 gausses. 9°7S 141. Fig. 112 represents diagrammatically the arrangement of magnetic circuits through the machine, where M, M y M, M t represent the field magnet cores, P y P' the pole-pieces and A A M M FIG. 112. — DIAGRAM OF MAGNETIC CIRCUIT. the armature. Fig. 113, represents diagrammatically the voltaic analogue of the magnetic circuits, where M x M^ Af t M A are four batteries, whose E. M. Fs. correspond to the M. M. Fs. of the field-magnet coils. M x and M t9 form one circuit through the field frame, a certain mean length of the pole-pieces, and a mean length in the armature a, together with the two resist- ances R x 7?, in the air-gaps. A similar circuit is provided for the E. M. Fs. M % and M through the air-gap resistances 7?, R v and the mean lengths of armature and pole-pieces. The equivalent arrangement of circuits is represented in Fig. 114, where M, M, are E. M. Fs., each equal to M, in the preceding figure, while the resistance of the double circuit through the field frame is one half of that of either of the resistances repre- sented in Fig. 113. 142. The flux through the field cores will be greater than the flux through the armature by reason of a certain leakage which occurs over the surface of the magnetic circuit. This leakage Digitized by VjOOQ IC 132 ELECTRO-DYNAMIC MACHINERY. is represented diagrammatically in Fig. 113, as taking place in a branch circuit or dotted semi-circle around the field coils, but, in reality, the leakage takes place in an extended system of branched or derived circuits between the polar surfaces and portions of the entire field frame. The calculation of the vari- ous reluctances in the air-path offered to leakage is very com- plex, and it is preferable, rather than to attempt such calcula- tion, to refer to experimental data already acquired with machines of similar type. The leakage factor, or the ratio of total flux through the field magnet cores to the total flux pass- FIG. II3. — VOLTAIC ANALOGUE OF' MAGNETIC CIRCUIT. ing from them through the armature, for a machine of this type, is approximately 1.7 ; so that, since the useful flux passing through the armature from each circuit M x M t and M % M Fig. 113, is 0.75 megaweber, the flux through the field cores may be taken as 0.75 x 1.7 = 1275 megawebers. The cross-section of the cores is found to be 176.8 sq. cms., so that the inten- . , . 1.275 X io* sity in them is, approximately, — , R = 7,211 gausses. 143. The reluctivity of the soft wrought iron armature at a density of 1.5 kilogausses, is, approximately, 0.0045 (Fig. 47), the mean length of the flux paths through the armature 38 cms., and the cross section 498 square cms. The reluctance of each side of the armature a, Figs. 113 and 114 is, therefore, ? — X Q-Q°45 == 0.000343 oersted. The joint reluctance of the 49 8 Digitized by VjOOQ IC WINDINGS OF A GRAMME-RING DYNAMO. 133 armature will, therefore, be 0.00017 oersted ; and, since the armature does not consist of continuous sheets of iron, but of / wires, and the flux has to penetrate from wire to wire down- ward through small air-gaps, the total effective reluctance of the armature will be approximately 0.001 oersted. The length of the air-gap or entrefer, is 1.22" =3.1 cms., and the area as already determined, 907. 5 sq. cms. so that the reluctance in % 1 * each air-gap will be — — =0.003416 oersted, the total reluc- * v 907s tance in the air, as seen in Fig. 1 10, will then be 0.006832 oersted. The reluctivity of the cast iron in the field frame at a mean intensity of 7,211 gausses, may be taken as 0.009 (Fig. 47). The length of the mean path in the field on each side of the machine is, approximately, 152.4 cms., and its cross-sectional area 176.8 sq. cms. ; so that the reluctance in each half of the field will be, approximately, — ~\ x 0.009 = 0.00776 oersted. 170.0 The total flux being divided between the two sides of the field, the joint reluctancfe, as represented in Fig. 114, will be 0.00388 oersted. The drop of magnetic poten- tial in the reluctance of the Gilberts. armature (# R) will be, . . . 1.5 x io* X 0.001 = 1,500 The drop of magnetic poten- tial in the reluctance of the the air, 1.5 X io* X 0.006832 = 10,248 The drop of magnetic poten- tial in the reluctance of the field, 2.55 x io* x 0.00388 = 9,894 Total 21,642 Since one gilbert = 0.7854 ampere-turn, the total M. M. F. in the circuit will have to be very nearly 17,000 ampere-turns, or 8,500 ampere- turns on each of the spools M, M, M, M. 144. The preceding calculation is open to errors from several sources in the absence of definite experimental data, namely : Digitized by VjOOQ IC 134 ELECTRO-DYNAMIC MACHINERY. (i.) The assumed leakage factor may be inaccurate. (2.) The mean lengths of the flux paths in various portions of the circuit may be inaccurate. (3.) The assumed increase in the reluctance of the armature FIG. II4. — DIAGRAM OF VOLTAIC ANALOGUE. due to its being formed of wires instead o*f solid sheets may be inaccurate. (4.) The reluctivity of the cast iron employed in the machine may not be that of the sample of cast iron assumed. In this, as in all constant-current machines, means are pro- vided for maintaining a nearly constant current strength in the circuit, despite changes in the load, but a consideration of such means, and of the requirements of the magnetic circuit to per- mit such regulation, will preferably be postponed until arma- ture reaction has been studied. Digitized by VjOOQ LC CHAPTER XIII. MULTIPOLAR GRAMME-RING DYNAMOS. 145. A given type of bipolar Gramme machine having proved satisfactory as regards efficiency, ease of running and cost, at a full-load output of say 10 KW, it may have to be determined whether it would prove advantageous to maintain the same design for a machine of a greater output, say 80 KW. Let us assume that the linear dimensions of the 10-KW machine are doubled, with the same speed of revolution, say 1,000 revolu- tions per minute, maintained in the larger machine. Then, assuming the same magnetic intensity in the armature, the electromotive force will be four times as great, since the area of cross-section of the armature, and, consequently, the total useful flux, will be increased fourfold. The resistance of the armature will be halved; for each turn, though twice as long, will have a cross-sectional area four times greater. The electric capability of the smaller machine being ex- e* (\eY pressed by — (Par. 6), that of the greater will be )^- = 32 — , or 32 times greater than in the 10-KW machine ; and, if the same relative efficiency is maintained in the larger machine the output will be 32 times greater. The weight of the larger machine would, of course, be eight times that of the smaller, and the output per pound of weight would, therefore, be four times greater in the larger machine. In reality, however, such a result is impracticable, as will now be shown. 146. Dynamo machines are either belt-driven or direct-driven. In the % case of direct-driven generators, the speed of the generator is necessarily limited by the speed of the engine, and this, for well-known constructive reasons, has to be main- tained comparatively low, and the larger the generator the slower the speed of rotation that has to be practically adopted. 135 Digitized by VjOOQ LC 136 ELECTRO-DYNAMIC MACHINERY. Thus, while a 100-KW generator is commonly driven direct from an engine at a speed of about 250 revolutions per minute, a 200- KW generator is usually direct 'driven at about 150, and a 400-KW generator at about 100 revolutions per minute. In the case of belt-driven generators, the speed of belting is usually limited, except when driving alternators, to about 4,500 feet per minute ; and, since larger generators require larger pulleys, their speed of rotation has to be diminished. While no exact rule can be applied for determining their speed, yet roughly, in American practice, the speed varies inversely as the cube root of the output, so that, when one generator has eight times the output of another of the same type, the speed of the greater machine would roughly be half that of the smaller. If no other limitation existed besides efficiency, the effect of doubling the linear dimensions of any generator, even taking the reduced rotary speed into account, would result in pro- ducing about sixteen times the output for eight times the total weight; but large machines must necessarily possess a higher efficiency than small machines, not only owing to the fact that they would otherwise become too hot, the surface available for the dissipation of heat only increasing as the square of the linear dimensions, while the weight and quantity of heat increase as the cube of the dimensions, — but also because large machines are expected to have a higher efficiency from a com- mercial point of view. 147. Taking into account, therefore, the reduced rot ar y speed of larger machines, their limits of temperature elevation, and their necessity for an increased efficiency, the output only increases, approximately, as the cube of their linear dimen- sions ; and, consequently, the output of the larger machine, per pound of weight, remains practically the same as that of the smaller. The output of belted continuous-current genera- tors is commonly six watts per pound of net weight, and of direct-driven multipolar generators about eight watts per pound of net weight. « 148. We have already seen (Par. 132) that the E. M. F. generated by a Gramme-ring armature, is # n w C. G. S. units, Digitized by VjOOQ IC MULTIPOLAR GRAMME RING DYNAMOS. 137 or # — 5 volts, and the resistance of the armature will be — io' 4 ohms, if R, be the resistance of the winding measured all the way round. Suppose now, that instead of employing a bi- polar machine, we double the number of poles and produce a four-pole or quadri polar machine, as shown diagrammatically in Fig. 115. If we employ the same total useful flux $, through each pole, the average rate of change of flux through the turns on the armature will be doubled, since the flux through any turn is now completely reversed in one-half of a revolution, FIG. II5. — DIAGRAM OF MAGNETIC CIRCUITS IN QUADRIPOLAR GRAMME GENERATOR. instead of in one complete revolution as before. The average E. M. F. in each turn will therefore be doubled. In Fig. 115 the magnetic circuits of a quadripolar Gramme generator are shown diagrammatically by the flux arrows. Here, as will be seen, four distinct magnetic circuits exist through the armature, instead of the two which always exist in the armature of a bipolar generator. In this type of field frame four magnetizing coils must be used. These may be obtained in one of two ways ; namely, (1.) By placing the magnet coils directly on the field magnet cores, as shown in Fig. 116; or, (2.) By placing one coil on each yoke, as represented in Fig. 117. Digitized by VjOOQ LC 138 ELECTRO-DYNAMIC MACHINERY. 149. In the same way, if we employ a field frame with six magnetic poles, as shown in Fig. 118, the flux will be reversed through each turn of wire three times in each revolution, and, consequently, the average E. M. F. in each turn will be in- creased threefold over that of a bipolar armature. In Fig. 118 there are six magnetic circuits through the armature. Considering any segment of the armature underneath a pole FIG. Il6.— QUADRIPOLAR GENERATOR WITH GRAMME ARMATURE. as, for example, between n^ and /, the turn occupying the posi- tion at « a , is filled with flux in an upward direction. As the armature advances in the direction of the large arrows, the flux through this turn will be diminished, and, when /it reaches the middle of the pole piece S 9 , it will be completely emptied of flux. The E. M. F. in the loop, during this portion of the revolution, will be directed outward on the ring, as shown by the double-headed arrows. After passing the centre of the pole piece S % , the flux through the loop begins to increase, but Digitized by VjOOQ LC Digitized by VjOOQ IC 140 ELECTRO-DYNAMIC MACHINERY. now in the opposite direction, the flux passing downward through the loop instead of upward as before, and, as we have already seen, flux entering a loop in one direction produces the same direction of E. M. F. around the loop as flux oppo- sitely directed withdrawing from the loop (Par. 105). Conse- quently,, the E. M. F. is still directed outwards on the ring, as indicated by the double-headed arrows, until the turn reaches the position /j. In other words, the E. M. F. in a loop is simi- FIG. Il8. — DIAGRAM OF SIX-POLE GRAMME-RING ARMATURE AND E. M. FS. larly directed during its motion toward and from the same pole; 1. e. y during its passage past a pole. When, however, the turn begins to approach the pole N x , after being completely filled with the downward flux at/,y /. e. y as the flux in it begins to decrease, the direction of the E. M. F. in it reverses, as shown by the double-headed arrows, and this direction of the induced E. M. F. continues until the turn reaches the position n x . By tracing the directions of the induced E. M. Fs. in the various turns of the ring, as shown, it will be seen that the positions /„ /„ and/ a , are points at which the E. M. F. is positive, or directed outwards, while the positions «,, « a , and n i9 are points at which the E. M. F. is negative, or directed inwards. There will be no current passing through the armature in the con- dition represented, if the winding of the armature be sym- metrical, since the E. M. Fs. in the various segments must be equal and opposite. If, however, brushes be applied to the Digitized by VjOOQ IC MULTIPOLAR GRAMME-RING DYNAMOS. \\l surface of the armature at the positions/,, /„ p %y and n l9 n % , « t , any pair of these, including one positive and one negative brush, will be capable of supplying a current through an ex- ternal circuit. 150. When, therefore, an ordinary Gramme-ring winding is employed, there will be one brush placed between each pair of poles, or, in all, as many brushes as there are poles. Fig. 119 FIG. II9. — DIAGRAM OF CONNECTIONS BETWEEN BRUSHES OF A SIMPLE GRAMME-RING WINDING OF A SEXTIPOLAR ARMATURE. represents the connections employed to unite the various seg- mental E. M. Fs. The E. M. F. of the armature is equal to that of one of its segments, but the resistance of the armature is in- versely as the number of segments and poles, and if R y be the resistance of the entire armature winding, -^ will be the joint resistance between brushes, for there will be / sections in parallel, each of which will have — ohms. Consequently, in a six-pole armature, there will be six segments in parallel, each having a resistance of —, making the joint resistance R R 5? or 6* Fig. 120 represents the mechanical arrangement for rigidly supporting the armature of a direct-driven octopolar Gramme- ring generator with eight sets of brushes pressing upon one side of the armature, thus dispensing with the use of a separate Digitized by VjOOQ LC 142 ELECTRO-DYNAMIC MACHINERY, commutator. The central driving pulley PPP> supports upon its arched face two rings R,R'. These rings clamp between them the armature core, and are clamped together by 14 stout bolts. Where the supports ss, interfere with the winding of the conductor inside the armature, the conductors are carried on the supports as at a b c and d. FIG. I20. — GRAMME-RING MULTIPOLAR ARMATURE. 151. It is not absolutely necessary, however, to employ six brushes in a sextipolar machine ; for, since in a machine of this type the three separate circuits are connected in parallel, con- nections may be carried within the armature between the various segments, permitting of the use of a single pair of brushes. Thus Fig. 121 represents a Gramme-ring armature, wound for a sextipolar field, with triangular cross-connections between its turns. In this case, the corresponding points/,, A> A> anc * n i> n *> n v °* Fig. 118, instead of being connected to- Digitized by VjOOQ IC MULTIPOLAR GRAMME-RING DYNAMOS. 143 gether by brushes externally as in Figs. 1 19 or 120, are connected together by wires internally. It is not, of course, necessary that every turn on the armature should be so cross-connected, but that the coils or group of turns which are led to the com- mutator should be cross-connected, so that each of the 36 turns, shown in Fig. 121, may represent a coil of many turns. Although the brushes are shown in Fig. 121, as beingplaced on FIG. 121. — ARMATURE CROSS-CONNECTIONS FOR A SEXTIPOLAR GRAMME-RING WITH TWO BRUSHES. adjacent segments, yet they may be equally well placed diametrically opposite to each other. Fig. 122 represents the corresponding cross-connections for a quadripolar Gramme generator, employing a single pair of brushes. The advantage of cross-connections is the reduction in the number of brushes. The disadvantage of cross-connec- tions lies in the extra complication of the armature connections. In large machines it is often an advantage to employ a number of brushes in order to carry off the current effectively. 152. Fig. 123 is a representation of a sextipolar generator whose magnetic field is produced by three magneto-motive forces, developed by coils placed as shown. The flux paths are represented diagrammatically by the dotted arrows at A. Each M. M. F. not only supplies magnetic flux through the segment of the armature immediately beneath it, but also con- tributes flux to the adjacent segments in combination with the neighboring M. M. Fs. Digitized by VjOOQ LC 144 ELECTRO-DYNAMIC MACHINERY, 153. From the preceding considerations it is evident that while it is possible to design a bipolar .generator for any desired output, yet, in practice, simple bipolar generators are not employed for outputs exceeding 150 KW, and, in fact, are seldom employed for more than 100 KW, since their dimen- sions become unwieldy and their output, per pound of weight, smaller than is capable of being obtained from a well-designed multipolar machine. In the same way, a quadripolar generator can be made to possess any desired capacity; but, in the United States, FIG. 122. — CROSS-CONNECTIONS FOR QUADRIPOLAR GRAMME-RING WITH TWO BRUSHES. practice usually increases the number of the poles with an increase in the output of the machine. Thus, it is common to employ a four-pole or six-pole generator for outputs of from 25 to 100 KW, and 8 to 12 poles for a generator of 400 KW, capacity. 154. Should the armature of a multipolar generator not be concentric with the polar bore ; i. e., if it is nearer one particu- lar pole than any of the others, the reduction in the length of the air-gap opposite such pole, will reduce the reluctance of that particular magnetic circuit, and by reason of the increased flux through the armature at this point, induce a higher E. M. F. in the segments of the armature adjacent to the pole Digitized by VjOOQ IC MULTIPOLAR GRAMME-RING DYNAMOS. 145 than in the remaining segments. If the armature be not inter- connected; i. e. y if it employs as many, pairs of brushes as there are poles, these unduly powerful E. M. Fs. can send no cur- rent through the armature as long as the brushes remain out of contact with the conductors; for an inspection of Figs. 118 and 119 will show that no abnormal increase of E. M. F. can exist in a single segment, but must be simultaneously generated in adjacent segments, and that such pairs of E. M. Fs. will counterbalance each other. When, however, the brushes are brought into contact with the armature conductors, thereby bringing the various segments into multiple connection with FIG. 123. — SEXTIPOLAR GRAMME-RING SUPPLIED BY THREE MAGNET COILS. one another, a tendency will exist for the more powerful E. M. F. to reverse the direction of current through the weaker segments. 155. Whether this tendency will result in an actual reversal of current depends upon the difference of E. M. F. between the segments, their resistance, and the external resistance or load. Let A and B y Fig. 124, represent the E. M. Fs. of any two segments in a multiple-connected Gramme-ring armature, and let the E. M. F., E, of A, be greater than the E. M. F., E\ of B. Owing to drop of pressure in the internal resistance r, the pressure e y at the terminals p y q, will be less than the E. M. F., E, of the stronger segment A. If e, is greater . pi than E\ a current of amperes will pass through the Digitized by VjOOQ IC 146 ELECTRO-DYNAMIC MACHINERY. segment B, in the direction opposite to that in which its E. M. F. acts. If e, be equal to E\ there will be no current through the segment B, while if e, be less than E\ a current will be sent through B, in the direction in which its E. M. F. acts, but of strength less than that supplied by segment A. Thus, in Fig. 125, the E. M. F., E, of the stronger segment A, finish ^^^wvvvw FIG. 124. — DIAGRAM OF E. M. F8. IN ADJACENT ARMATURE SEGMENTS. is represented by the ordinate e + d. Owing to the resist- ance r, in the segment A, a drop of pressure d, will take place within it, and the pressure at its terminals will be e volts. If E' be less than e, the stronger segment A, will send a cur- rent back through the segment B, while if E\ be greater than , of th ohm; then, provided its four magnetic circuits are balanced or equal, the full load on each , segment will be 250 amperes, and the drop in each 2.5 volts; so that the four E. M. Fs. will be, Fig. 126 : Wasted Power. Watts. 625 625 625 625 I,OOb 2,500 E. M. F. Drop. Current. Volts. Volts. A ntperes. A = I02.5 2.5 250 B =. I02.5 25 250 C = IO2.5 ' 2.5 250 D = I02.5 2.5 250 Digitized by VjOOQ IC MULTIPOLAR GRAMME-RING DYNAMOS. 147 The power expended in each segment of the armature by 250 X 250 the current as PR, will be — — = 625 watts, and the 100 total PR loss in the armature, 2,500 watts. 156. Considering one of the segments, say C, as normal, and that A y owing to the magnetic dissymmetry, gives an E. M. F. two volts in excess; £, one volt in excess; and D> one volt in FIG. 126. — DIAGRAMMATIC ARRANGEMENT OP E. M. Fg. IN THE SEGMENTS OF A QUADRIPOLAR ARMATURE. deficit; the excitation necessary for 1,000 amperes total out- put will produce (Fig. 127) the following conditions; namely, E. M. F. Volts. Drop Volts. Load. A mferes. Wasted Power. Watts. A = 104 4 400 1,600 B = IO3 3 300 9OO C = I02 2 2O0 4O0 D = IOI I IOO IOO 1,000 3,000 157. The effect of magnetic dissymmetry in the segments, under the assumed difference of three volts, will produce, at 4nn& FIG. 127. — DIAGRAMMATIC ARRANGEMENT OF E. M. Fs. IN THE SEGMENTS OF A QUADRIPOLAR ARMATURE. full load, a difference of output among the segments, ranging from 100 to 400 amperes, while the total power wasted in the armature winding will be increased 20 per cent. ; namely, Digitized by VjOOQ LC 148 ELECTRO-D YNAMIC MA CHINE R Y. from 2,500 to 3,000 watts. The armature will, therefore, be raised to a higher temperature, owing to the magnetic dis- symmetry, but this increase in temperature will not be localized, since, although at one moment a greater amount of heat is being produced in certain segments than in others, yet, owing to the rotation of the armature, the portions of the armature constituting these segments are constantly changing. 158. Suppose now the external circuit be entirely removed, the brushes remaining in contact with the conductors (Fig. 128) FIG. 128. — DIAGRAMMATIC ARRANGEMENT OF E. M. FS. IN THE SEGMENTS OF A QUADRIPOLAR ARMATURE. so that the circuits through the armature segments are com- plete ; then the following conditions will hold : E. M. F. Volts. Drop. Volts. Current. A mperts. Wasted Power. Watts. A = IO4 1.5 ISO 225 B = IO3 0.5 50 25 C = I02 -O.5 -50 25 D = IOI -1-5 -I50 225 o 500 An inspection of these values shows that a difference of three volts between the E. M. Fs. of the four segments, pro- duces a reversal of current through Cand Z>, at no load, with a useless expenditure of 500 watts. Consequently, between no load and full load, there will be a change from an expenditure of power with reversal of current in the weaker segments, to an excessive drop and expenditure of power without reversal of current. 159. Although this difficulty, arising from the unbalanced magnetic position of the armature, does not, in practice, give Digitized by VjOOQIC MULTIPOLAR GRAMME-KING DYNAMOS. 149 rise to any serious inconvenience, when mechanical construc- tion is carefully attended to, yet windings have been devised by which it maybe altogether avoided. For example, if all the turns be so connected that their £. M. Fs. are placed in series, then a single pair of brushes will be capable of carrying the current from the entire armature, which will only be divided into two circuits; or, the segments may be so interconnected that turns in distant segments may be connected in series so as to obtain a more general average in the total E. M. F. Such windings are always more or less complex, and the reader is referred to special treatises on this subject for fuller details. 160. The formula for determining the E. M. F. of a multi- polar Gramme generator armature is, E = $nw C, G. S. units, where 4>, is the useful flux in webers, or the flux entering the armature through each pole, «, the number of revolutions per second of the armature, and w, the number of turns on the surface of the armature counted once around. If, however, the armature be series connected, so that instead of having /, circuits through it between the brushes, where/, is the number of poles, there are only two circuits, then the E. M. F. will be E = — $nw f while if, as in 2 some alternators, the circuit between the brushes be a single one, the mean E. M. F. of the armature will bep$nw. z6l. Fig. 129 represents the magnetic circuits of an octopolar generator, the dimensions being marked in inches and in centi- metres. The field frame is of cast steel, and the armature core is formed of soft iron discs. Let us assume that there are 768 turns of conductor in the armature winding, and that the speed of rotation is 172 revolutions per minute, or 2.867 per second. Assuming an intensity of 9,500 gausses in the armature, it may be required to determine the E. M. F. of the machine. The cross-section of the armature is 31.1X13 = 404.3 sq. cms., but allowing a reduction factor of 0.92 for the insulating material between the discs, the cross-section of iron is 372 sq. cms. The total flux passing through the cross-section of Digitized by VjOOQ LC 15© ELECTRO-DYNAMIC MACHINERY. the armature will, therefore, be 372 x 9,500 = 3,534,ooo webers. The useful flux through each pole will be twice this amount, or 7,068,000 webers, so that the E. M. F. of the generator will be : E = $mv = 7,068,000 X 2.867 X 768 = 1.557 X io 10 = 155.7 volts. This will be the E. M. F. of the generator, provided all the FIG. 129. — GRAMME-RING OCTO POLAR GENERATOR. armature segments are connected in parallel, as shown in Fig. 115. If, however, the armature winding be so connected that only a single pair of brushes and a single pair of circuits exist through the armature, the E. M. F. would be 4 times as great, while if the armature could be connected in a single series, the E. M. F. would be 8 times as great. 162. In order to determine the M. M. F. necessary to drive this flux through the armature we proceed as follows: viz., Digitized by VjOOQ IC MULTIPOLAR GRAMME-RING DYNAMOS. 151 We first determine the cross-section, the mean length, and the intensity in each portion of the magnetic circuits. One of the eight magnetic circuits through the armature is represented by the dotted arrows at A (Fig. 129). We may assume that the flux through the cores is 7,068,000 x 1.3 = 9,188,400 webers; 1.3, being the approximate leakage factor for a machine of this type; in other words, of all the flux passing through the cores — x 100 = 76.9 per cent, approximately, may be assumed to pass through the armature, half through each cross- section. Consequently, we have the following distribution : Field core, Yoke, . Armature, Cross-section. Flux. Intensity. Length Sq. cms. Webers. Gausses. Cms. *ml$*t 9,188,400 13,430 40 354^ 3,534.000 9,980 76 «**?7V 3,534»ooo 9,500 50 I *-- The entrefer, or gap, of copper, air and insulation, existing between the iron in the armature and in the pole faces, is 1.5 centimetres . in length, while the polar area . is 41 cms. X 34 cms., or 1,400 sq. cms. in cross-section. From these data, the reluctance in the magnetic circuit through the armature is Field core, Length. Cms. Intensity. Gausses. Reluctivity. Cross- section. Sq. cms. Cross-section carrying armature flux. Sq. cms. Reluctance. Oersted. 40 13,430 0.002 342* 263.I 0.000,304 40 13,430 0.002 342* 263.I 0.000,304 76 9,980 O.OOI J54" 354.0 0.000,215 1.5 I. 7001/ 0.002,142 1.5 I. 700 v 0.002,142 50 9,50O O.OO08 372" 372 0.000,107,5 0.005,214,5 Yoke, Entrefer, u Armature, The M. M. F. required to drive a total flux of 3,534,000 webers through this circuit will be 3,534,000 x 0.005,214, (i8. ,5= < 14, (7,3 430 gilberts. 665 ampere-turns. 333 ampere-turns on each spool. With 600 turns on each spool, the current would be 12.22 amperes. Digitized by VjOOQ IC CHAPTER XIV. DRUM ARMATURES. 163. The drum armature was first introduced into electrical engineering by Siemens, in the shape of the shuttle armature, and was modified by Hefner-Alteneck in 1873. The drum armature was subsequently modified in this country by the introduction of a laminated iron armature core, consisting of discs of soft iron, called core discs, provided with radial teeth or projections. This armature core, when assembled, had FIG. I30.— TOOTHED-CORE ARMATURE IN VARIOUS STAGES OF CONSTRUCTION. space provided between the teeth for the reception of the armature loops on its surface, a completed armature showing, when wound, alternate spaces of iron and insulated wire, and formed what is called a toothed-core armature. Next followed the smooth-core drum armature, that is, a drum armature com- posed of similar core discs in which the teeth were absent, so that the completed armature had its external surface com- pletely covered with loops of insulated wire. Fig. 130 shows a common type of toothed-core armature in various stages of construction. The laminated iron core is shown at A y as assembled on the armature-shaft ready to receive its winding of conducting loops in the spaces between the radially project- ing teeth. At £, is shown the same core provided with wind- Digitized by VjOOQ IC DRUM ARMATURES. 153 ings of insulated wire. At C, is shown a completed armature. The detailed construction of a laminated armature core is illustrated in Fig. 131, which shows a portion of a drum arma- ture core already assembled by the aid of large bolts^ passing FIG. 131. — TOOTHED-CORE ARMATURE IN PROCESS OF ASSEMBLING. through holes in the core -discs. On the right are other core-discs ready to be placed in position on the shaft. 164. Fig. 132 shows a laminated armature body of the smooth-core type. Here the separate core-discs are formed FIG. 132. — SMOOTH-CORE ARMATURE BODY. of sheet iron rings assembled on the .armature shaft as shown. These discs, after being assembled, are pressed together hydraulically. The end rings are heavy bronze spiders, held Digitized by VjOOQ IC '54 ELECT/tO-D YNAMIC MA CHJNER K together internally by six bolts shown in the figure. When the armature body is subjected to compression, these bolts are tightened on the spiders, which are firmly keyed to the shaft, so that on release of the hydraulic pressure, the lami- na. 133. — COMPLETED ARMATURE, SMOOTH-CORE TYPE." nated iron core forms one piece mechanically. Fig, 133 shows the same armature completely wound. 165* In the drum armature, the conducting wire is entirely confined to the outer surface, and does not pass through the FIG. I34, — TYPICAL iOKM OF SMALL SIZE PR CM ARMATURE. interior of the core, In this respect, therefore, it differs from the Gramme-ring armature, already described, in which the winding is carried through the interior of the core, lying, therefore, partly on the interior and partly on the exterior. The armature core, or body, of a Gramme-ring machine differs markedly in appearance from the jirmature body of a drum machine, when both arc in small sizes, since then the drum core is practically solid, having no hollow space, so that it would be impossible to wind it after the Gramme method. Such a drum- wound armature is shown in Fig, 134, When, however, Digitized by VjOOQ IC DRUM ARMATURES. *55 the drum armature is increased in size, so as to be employed in multipolar fields, the form of the core or body passes from a solid cylinder to that of an open cylinder or ring, as is shown in Figs. 132 and 135, so that it would be possible to place a conducting wire on such a core either after the drum or Gramme type of winding. The tendency, however, in modern electrical engineering is, perhaps, toward the produc- tion of drum-wound rather than Gramme-wound generators. FIG. I35. — LARGE DRUM ARMATURE FOR MULTIPOLAR FIELD. This tendency has arisen, probably more from mechanical and commercial reasons than from any inherent electrical objections. to armatures of the Gramme-ring type. 166. The windings of drum armatures are numerous and complicated in detail, but all may be embraced under two typi- cal classes ; namely, lap-winding and wave-winding. In lap- winding, the wire is arranged upon the surface of the armature in conducting loops, the successive loops overlapping each other, hence the term; while in wave-winding, the conducting Digitized by VjOOQ IC 156 ELECTRO-DYNAMIC MACHINERY. wire makes successive passages across the surface of the armature, while being advanced around its periphery in the same direction. 167. Lap-winding is applicable particularly to bipolar arma- tures, while wave-winding is applicable only to multipolar armatures. b FIG. I36. — SIMPLE BIPOLAR DRUM-WINDING. The simplest form of lap-winding is shown in Fig. 136, where the separate paths taken by the turns a, b, c, d, and e, f, g> A, across the outside of the bipolar armature core, and their con- nections to the commutator, are represented as shown. If the ~d FIG. I37. — SIMPLE BIPOLAR DRUM-WINDING WITH LEAD IN COMMUTATOR CONNECTIONS. entire winding of the armature be completed, it is evident that any attempt to represent the winding graphically by the method adopted in this figure would lead to great complexity. For this reason it is customary to represent the armature sur- face as unrolled, or developed upon the plane of the paper, as Digitized by VjOOQ LC DRUM ARM A TURES. *57 shown in Fig. 138. For example, the winding already shown in Fig. 136 becomes on this development represented as in Fig. 138. Here it ii clear that each loop overlaps its prede- b *^k 1 v ! ^ - -f- c r 1 ! 1 1 a e |i d FIG. 138. — DEVELOPMENT OF LAP-WINDING IN FIGS. 136 AND 137. cessor, and, consequently, it is evident that the simplest form of drum-winding is a lap-winding. Fi 8- J 37 represents the same winding as Fig. 136, except d * 9 FIG. I39.— QUADRIPOLAR WAVE-WINDING. that the connections with the commutator are given a lead of 90 degrees, requiring a correspondingly altered position of the brushes of the machine. Fig. 139 represents a number of conductors, at, cd, ef, gh, Digitized by VjOOQ LC 158 ELECTRO-DYNAMIC MACHINERY. etc., wound on the external surface of a drum core in the winding of the wave type. Here it will be seen that the conducting wire, after crossing over from one side of the armature core to the other, advances progressively over its surface in the form of a rectangular wave. The corre- sponding development is shown in Fig. 140. The winding shown is applicable only to multipolar fields ; for, an inspec- FIG. 140. — DEVELOPMENT OF QUADRIPOLAR WAVE-WINDING. tion of this particular arrangement of wave-winding will show- that when conducting wires ab and 83,860 00,330 96,770 103,900 X09,7O0 Il6,IOO Gausses[(B]. 10,000 IX,O0O 13,000 13,000 14,000 15,000 16,000 17,000 z8,ooo Watts, per cc. -4 6.38x10 -4 7.3IXIO -4 8.40x10 -4 9.55x10 -» 1. 06x10 -s I.30XI0 -• I.33XIO -3 X^7XIO -» 1. 61x10 Watts, per cubic in . . . -» 1.03x10 -■ X.30X10 -t 1.38x10 1.57x10 -t 1.76x10 -• I.97XIO -■ 3.l8xiO -8 3.4IXIO -• 3.64x10 Watts, per lb. -t 3.65x10 -» 4.35XIO -t 4.89x10 -s 5.56x10 -t 6.s6xxo -■ 6.79XIO -■ 7.75XXO -■ 8.53XIO -• 9.35x10 190. As an example of the hysteretic activity, we may con- sider a pound of iron subjected to a periodic alternating flux density of ten kilogausses, with a frequency of 25 cycles-per second. From the preceding table, it is seen that at 10 kilo- gausses the hysteretic activity is 0.0365 watts-per-pound, at a frequency of one cycle per second. At 25 cycles per second this would be 25 x 0.0365 =0.9125 watt = 0.9125 joule-per- second = 0.6735 foot-pound per second. Consequently the hysteretic activity might be represented by lifting the pound at the rate of 0.6735 f° ot P er second against gravitational force. If, therefore, all the iron in an armature core be subjected to an intensity of ten kilogausses, and rotates 25 times per second in a bipolar field, 12.5 times per second in a quadripolar field, MAGNETIC HYSTERESIS. 175 Title Showing the Hysteritic Activity in Good, Soft Sheet Iron or Steel Undergoing One ComyUte Magnetic Cycle per Seconds in Watts per Cubic Centimetre, Watt* per Cubic Inch, and Watt* per Pounds /or Various Mafnetic Intensities in Gausses and in Webers Per Square Inch. Webers, per > sq. in 6.45a 13,900 19,360 35,8lO 33,300 1 38.7*0 45,16© 51,630 58,060 Gausses[C&], 1,000 3,000 3i°°° 4,000' 5,000 6,000 7,000 8,000 9,000 Watts, per cc. Watts, per cubic in. . . Watts, per lb. -§ 1.58x10 -4 3.59x10 -1 9.17x10 -• 4.78XIO -4 7.84XIO -3 3.78XIO -• 9.15x10 -8 1. 5OXIO -» 5.33XIO -4i -4 L45XIO .3.07X10 -8 -8 3.38X10 3.4OXIO 1 -31 -8 8.43x10 jI.SIXlO -4 3.78x10 -8 4.55*"> -8 I.63XIO -4 3-55X"> -3 5.83x10 -8 3.O0XIO • -4 4.4OXIO -3 7.90X10 -8 3.56X10 -4 5.3I*IO -» 8.69XIO -8 3.O9XIO T - S Digitized by VjOOQ IC 176 ELEC TRO-D YNAMIC MA CHINER Y. or 6.25 times per second, in an octopolar field, hysterei activity is being expended at a rate which is probably repi sented by the activity of raising the whole armature coreabo eight inches per second. It is to be observed that the table represents average samp] of good commercial iron, and by no means the best quality iron obtainable. 191. As an example of the application of this table, suppo that it is required to estimate the power expended in hysterei during the rotation of the armature of the octopolar generat represented in Fig. 129, the weight of iron in the armatu being 2,700 lbs. At the maximum intensity of 9,500 gausses, or 61,290 webe: per-sq. in., the table shows that the hysteretic activity p pound at one cycle per second is about 3.4 X io~ f watts, each revolution of the armature there would be eight reversa or four complete cycles, and at 2.867 revolutions per secon the frequency of reversal would be 11.468 cycles per secon The total hystcrcti c^activity is, therefore, P X 2,700 X 3-4 X io-" X 11.468 = 1,053 watts. This would be the hysteretic activity in the armature wh generating 155.7 volts. When generating a lower E.M.F., t flux intensity in the armature would be reduced, and, therefoi the hysteretic activity. 192. Hysteresis, therefore, occurs when a mass of ir undergoes successive magnetizations and demagnetizatioi and this is true whether such are caused by the reversal of t magnetizing current, with the mass at rest, or by the reversal the direction of the mass in a constant magnetic field. Cons quently, the revolutions of the armature of a dynamo or mote occasioning the successive magnetizations and demagneti ations of its core, are accompanied by an hysteretic loss energy. The amount of this hysteretic. loss increases directly with t volume V, of iron in the armature in c. c, the number «, revolutions of the armature per second, the hysteretic coei cient rj of the iron employed, and the 1.6th power of t maximum magnetic intensity in the iron; for, it is evident th Digitized by VjOOQ LC MAGNETIC HYSTERESIS. *77 in one complete revolution of the armature its direction of magnetization will have undergone two reversals, provided that the field is bipolar. In a multipolar field the number of revers- als increases with the number of poles/, and the hysteretic activity becomes P = V nri p<$> 1 watts. In the case of a gen- erator, this activity must be supplied by the driving power, and in the case of a motor by the driving current FV^ 193. When a generator armature is at rest in an unmagnet- ized field, the torque; i. e., the twisting moment of the force which must be applied to the armature in order to rotate it, is such as will overcome the friction of the journals and brushes. When, however, the field is excited, so that the armature becomes magnetized, the torque which is necessary to rotate the armature is increased, even when the armature is symmet- rically placed in regard to the poles. This extra torque is due to hysteresis. It is sometimes called the hysteretic torque, and is equal to _ Vy/dS 4 n megadyne-decimetres. 194. The total useless expenditure, therefore, of power in an armature core is the sum of the hysteretic and eddy current loss. The former increases as the speed of revolution directly, but the latter, as already pointed out, increases as the square of the speed. Consequently, if we have an unwound armature core, and rotate it on its shaft through a field which is at first unexcited, we expend an activity which might be measured, and which would be entirely frictional loss. When the field is ex- cited, we expend activity against mechanical friction, hysteresis and eddy currents combined. By varying the speed of rotation, and observing the rate at which the activity given to the rotat- ing armature increases, it is possible to separate the three descriptions of losses from each other. m i ■/•..'. ■■ 195. Although, as we have seen, the hysteretic loss increases with the 1. 6th power of the intensity of flux, yet it is stated to have been found experimentally, that when a mass of iron, such as an armature, is rotated in a sufficiently powerful magnetic Digitized by VjOOQ IC 178 ELECTRO-DYNAMIC MACHINERY. field, the hysteretic loss entirely disappears, owing to the si posed rotation of all the elementary molecular magnets abc their axes during the rotation of the armature without losi parallelism, and, consequently, without any molecular os< lation and expenditure of magnetic energy as heat. So as experiments have yet shown, this critical intensity in t iron is above that which ordinary dynamo or motor armatui attain, so that under practical conditions, the 1.6th power the maximum intensity determines the hysteretic loss. 196. From an examination of the formula expressing t hysteretic activity in the armature, it is evident that t activity might be decreased by a decrease either in the numt of poles, the speed of revolution, the flux density, or the h; teretic coefficient. Since, however, in any machine the fii three factors are practically fixed, it is important that t remaining factor, or hysteretic coefficient, should be kept low as is commercially possible. For this reason, whene\? the hysteretic loss is a considerable item in the total losses the generator, care is taken to select the magnetically soft* iron commercially available, in which the hysteretic coefiicie is a minimum. 197. We have already referred to the increase in tempei ture of the edges of the field-magnet poles during the operati of a dynamo armature, and have ascribed the cause of su heating to the development of eddy currents locally produc there. It is to be remarked, however, that some of the he in such cases may usually be ascribed to true hysteretic chang in magnetization. Digitized by VjOOQ IC CHAPTER XVIII. ARMATURE REACTION AND SPARKING AT COMMUTATORS. 198. In the operation of a dynamo-electric generator, con- siderable difficulty is frequently experienced from the sparking which occurs at the commutator, that is to say, instead of the current being quietly carried off from the armature to the external circuit, a destructive arc, which produces burning, occurs between the ends of the brushes and the commutator segments. The tendency of this sparking, unless promptly checked, is to grow more and more marked from the mechani- cal irregularities produced by the pitting and uneven erosion FIG. I49. — GRAMME-RING ARMATURE IN BIPOLAR FIELD ON OPEN CIRCUIT. of the commutator segments. It becomes, therefore, a matter of considerable practical importance to discuss the causes of sparking at the commutator, and the means which have been proposed, and are in use, to overcome the difficulty. 199. When a Gramme-ring armature, such as that shown in Fig. 149, is rotated on open circuit, in a uniform bipolar field, the brushes, when placed on the commutator, must be kept at diametrically opposite points corresponding to the line n n. If applied to the commutator at any other points, sparking will probably occur, although the armature is on open circuit. The reason for this is seen by an examination of the figure, which represents a pair of coils C, C", about to undergo com- Digitized by VjOOQ IC ■£: . an ''■'-■J -5 180 ELECTRO-DYNAMIC MACHINERY. mutation ; i. e. y about to be transferred by the rotation of t armature from one side of the brush to the other, and bei short circuited by the brushes, as they bridge over the adjac< segments of the commutator to which their ends are connect Since the coils C, C\ in the position shown, embrace i maximum amount of flux passing through the armature, th will be no E. M. F. induced in them, and, consequently, th< will be no current set up during the time of short circuit un< the brushes. In other words, the prime condition for m sparking at the commutator is that the coils shall be sh FIG. 150. — GRAMME-RING ARMATURE WITH BRUSHES DISPLACED FRO! NEUTRAL LINE. circuited only at the time, and in the position, where E. M. Fs. are being generated in them. 200. If the brushes be advanced into a position such as t represented in Fig. 150, so that the diameter of commutatit i. e., the diameter of the commutator on which the brushes re is shifted from B, B\ to a new position, powerful sparking w probably, be set up, for the reason that in this position 1 rate of change, in the flux linked with these coils, is consid able, and, consequently, there is a considerable E. M. induced in them, so that, when they are short circuited by brushes, heavy currents tend to be produced in the circuit these coils according to Ohm's law. If, for example, a bipc Gramme-ring armature gives passage to a total useful flux 1 megaweber, and there are 1,000 turns on the armatu and 50 segments in the commutator, then, if the speed of re tion be 10 revolutions per second, the E. M. F. set up betw< the brushes will be 10 X 1,000 x 1,000,000 100,000,000 volts, Digitized by VjOOQ LC i;:M ARMATURE REACTION. 181 and, since there are 25 commutator bars on each side of the diameter of commutation, there will be an average of four volts per coil of 20 turns. If the resistance of each coil be 0.01 ohm, the current which tends to be set up in a short- circuited coil having the average E. M. F. is -A_= 4 oo amperes. ^ i > 201. It now remains to be explained how the existence g • of a powerful current in the short-circuited coil will produce £:-.; violent sparking at the commutator. It is well known that jc the presence of a spark indicates a higher £. M. F. than the \.r four volts, which we have assumed in this case is to be gen- 5. erated in the short-circuited coil. The increase in the voltage [. at the moment of sparking is due to what is called the induct- * ance of the coil. ?"' At the moment of short circuiting the coil by the bridging of the brushes across the two adjacent commutator segments, a powerful magnetic flux is set up in the coil, owing to its M. M. F. This flux is so directed through the coil as to set up in it an *\ E. M. F. which opposes the development of the current. On the cessation of the current, owing to the breaking of the coil's circuit at the commutator, the coil is rapidly emptied of flux, * and a powerful E. M. F. is set up in the same direction as the current, sufficiently powerful to produce sparking between the brush and the edge of the segment it is leaving. The E. M. F. so generated during the filling or emptying of the loop by its own flux is called the £. M, F. of self-induction. 202. Fig. 151 diagrammatically represents the flux produced in the short-circuited coils C", C, by the M. M. F. of the current produced during the short circuit. This flux passes princi- pally through the air-gap and neighboring pole face, a small portion passing through the air in the interior of the armature between the core and the shaft. The greater the flux produced by the coil, the greater will be the E. M. F. developed in the coil, when the flux is suddenly withdrawn. The capability of a conducting loop or turn for producing E. M. F. by self- induction is called its inductance, and may be measured by the linkage of flux with the turn per ampere of the current it carries, that is, by the amount of flux passing through it. Digitized by VjOOQ IC 182 ELECTRO-DYNAMIC MACHINERY. i m 203. We have thus far considered the coils C, C\ as be composed of a single turn. If, however, each of these coil composed of two turns, and the same current strength pas through each of these turns, then the M. M. F. of the coil y be doubled, and, if the iron in the armature core and p face, is far from being saturated, the amount of flux pass through the two turns will be twice as great as that which p viously passed through one. When this flux is introduced removed it will generate E. M. F. in both turns, and, con quently, will induce twice as much E. M. F. in the two tu together as in a single turn. The inductance of th£ coil, or capacity for developing E. M. F. by self-induction, is thus f< times as great with two turns as with one, because there FIG. 151. — DIAGRAMMATIC REPRESENTATION OF FLUX IN MAGNETIC CIRC OF SHORT-CIRCUITED COIL. double the amount of flux, and^double the number of tu receiving that flux. 204* It is evident, therefore, that the inductance of a < increases rapidly with the number of its turns, and althot not quite proportionally to the square of the number, sin with a large number of turns, although the M. M. F. is creased in proportion to the number, yet the amount of f passing through each of the turns, owing to leakage, is not ' same. The E. M. F. of self-induction generated in each c depends: (1.) Upon the E. M. F. induced in the coil by the revolut of the armature. (2.) Upon the resistance of the coil, or its capability allowing a large current to flow through it. (3.) Upon the inductance of the coil, or its capability Digitized by VjOOQ LC A ARMATURE REACTION. 183 permitting that current to induce a powerful E. M. F. when the circuit is made or broken. The E. M. F. induced on making the circuit at the commu- tator is advantageous, since it checks the development of the current ; the E. M. F. induced on breaking the circuit is harmful, since it enables a spark to follow the brush. If, therefore, no sparking is to occur in a dynamo-electric machine at no load, the brushes must rest on segments, con- nected with coils in which no E. M. F. is being generated. 205. If the external circuit of the armature be closed through a resistance, so that current flows through the arma- ture coils and brushes into the external circuit, the preceding conditions become considerably modified. Fig. 152 represents the condition of affairs in which a current FIG. 152. — DIAGRAMMATIC REPRESENTATION OF MAGNETIC CIRCUIT OF ARMATURE. is flowing through the armature coils, and the brushes are resting on the commutator, with the diameter of commutation at the neutral points, or in a plane at right angles to the polar axis. In this figure the direction of the armature rotation is the same as shown in previous figures; namely, counter-clockwise. Here the flux produced by the M. M. F. of the armature coils takes place in the circuits digrammatically indicated by the curved arrows. The magnetization, therefore, produced by the current circulating in the armature turns, is a cross mag- netization, or a magnetization at right angles to the magnetiza- tion set up by the field flux. The field flux through the poles and armature is diagrammatically indicated in Fig. 153, where the north pole is assumed to be situated at the left-hand side 'My J-' • Digitized by VjOOQ LC 1 84 ELECTRO-DYNAMIC MACHINERY. of the figure, and the average direction of the field flux is right angles to the average direction of the armature flux. / inspection of Figs. 152 and 153 will show that at the leadi edges of the pole-piece, Z, Z', that is, at those edges of the pol piece which the armature is approaching, the direction of tl flux produced by the armature is opposite to that of tl FIG. 153. — DIAGRAMMATIC REPRESENTATION OF FIELD FLUX PASSING THROUGH ARMATURE. flux produced by the field, and that, consequently, the effe of superposing these fluxes is to weaken the flux at the leadii edge as is shown in Fig. 154. On the contrary, at thzfollowi edges F' and F, of the pole-pieces, the direction of the armatu FIG. 154. — EFFECT OF SUPERPOSING ARMATURE FLUX ON FIELD FLUX. flux coincides with the direction of the field flux, and the supe position of these two fluxes will have the effect of intensifyii the flux at the following edges. Consequently, the neutral h in the armature, or the line symmetrically disposed as regar the entering and leaving flux, will no longer occupy the po: tion JV 9 JV, at right angles to the polar axis, but will occupy position n n' ; therefore, in order to set the brushes so th they may rest upon commutator segments connected with co Digitized by VjOOQ LC ARMATURE REACTION. 185 having no E. M. F. generated in them, it is necessary to bring the diameter of commutation into coincidence with the neutral line, or to give the. brushes a lead; i. *., a forward motion, or in the direction in which the armature is rotating. 206. This, however, will not in itself, as a rule, prevent sparking, for the reason that induced E. M. Fs. are produced in the coil under commutation at load, even although* the coil being commuted has no resultant E. M. F. set up by rotation. This induced E. M. F. is due to the inductance of the coil and FIG. 155. — REVERSAL OF CURRENT IN ARMATURE COILS DURING COM- MUTATION. to the load current which it carries. An inspection of Fig. 155 will show that as the coil C, approaches the brush B y the current in the coil, as shown by the arrows, is directed upward on the side facing the observer; while on leaving the brush, after having undergone commutation, the current in the coil will be flowing in the opposite direction or downward. The sudden reversal of the current in the coil under commutation produces a sudden reversal of the magnetic flux linked with the local magnetic circuit of that coil, and this sudden change in the magnetic flux through the coil induces in it a powerful E. M. F., causing a spark to follow the brush. In order that no spark shall be produced from this cause, it is necessary that before the brush leaves the segment the cur- rent in the coil shall have become reversed, and will therefore be flowing in the same direction as that which will pass through it during its passage before the pole face N. In order to effect this it is necessary to bring the coil that is being commutated into a field of sufficient intensity to induce in it, while short circuited, a current strength equal and opposite to that which Digitized by VjOOQ IC i M m !-• I.: i.1 1 86 ELECTRO-DYNAMIC MACHINERY. passes when it first becomes short circuited by the brush, is not, therefore, usually possible to keep the brushes on tl neutral line as shown in Fig. 154, at n ri> but their lead mu be increased, until the coil under commutation is in a sufficient powerful field beneath the pole face to produce, or nearly pr duce, this reversal of current. The amount of lead necessa to give to the brushes in order to effect this will depend up< the inductance of the coils, and also on the strength of t current in the armature. 207. The lead of the brushes, besides tending to redu sparking at the commutator, tends to diminish the E. M. generated by the armature, for two distinct reasons : Fin because it connects in series armature windings in which t E. M. Fs. are in opposition, as will be seen from an examir tion of Fig. 156; and second, because the M. M. F. of t armature coils over which the lead has extended exerts C. M. M. F. in the main magnetic circuit of the field coi thereby tending to reduce the useful flux passing through t armature. This effect is called the back-magnetization of t armature. Cross-magnetization, therefore, exists in eve armature as soon as it generates a current, but back-ma netization only exists when a current is generated in the am ture, and the diameter of commutation is shifted from t neutral points. 208. The conditions which favor marked sparking at t commutator of a generator are, therefore, as follows; name! (1.) A powerful current in the armature; /. e., the sparki increases with the load. (2.) A large number of turns in each coil connected to t commutator; /. e., the sparking increases with the inductanc (3.) A great distortion of the neutral line through t armature, or a powerful armature reaction. (4.) A high speed of rotation of the armature, since t current in the coil has less time in which to be reversed duri the period of short circuiting. (5.) A nearly closed magnetic circuit for each coil;./.*, small reluctance in the magnetic circuit of each coil, where the inductance of the coil is increased. Digitized by VjOOQ LC ARMATURE REACTION. 1 87 The conditions which favor quiet commutation, or the absence of sparking, are as follows; namely, (1.) A small number of turns in each commuted coil, or a large number of commutator bars. (2.) Decrease of current strength through the armature. (3.) A lead of the brushes. (4.) A powerful field, or a high magnetic intensity in the entrefer, due to the M. M. F. of the field magnets. (5.) A large reluctance in the magnetic circuit of each coil. 209. An inspection of Figs. 152-154 will render it evident that the effect of superposition of the armature M. M. F. upo'n the M. M. F. of the field magnets, is to weaken the intensity of the field flux at the leading edges of the pole- pieces, and to strengthen the intensity at the following edges of the pole-pieces. At the same time, it is necessary to advance the brushes; /. e., the diameter of commutation, so as to bring the commuted coils under the leading edges of the pole-pieces, in order that they may receive a sufficiently powerful intensity of field flux to enable the armature current to be reversed in the coil under the brushes, and sparkless commutation thus to be effected. If, however, the number of ampere-turns on the armature; /. e. y its M. M. F. at a given load, be sufficiently great, the field flux at the leading edges of the poles will be so far weakened, that the intensity left there will be insufficient to effect sparkless commutation, no matter how great the lead may be. In other words, the flux from the armature will overpower the field flux, in any position of the brushes. This will take place when the M. M. F. due to half the turns of active conductor on the armature, covered by the pole face, is equal to the drop of magnetic potential in the field flux through the entrefer. 210. The magnetic intensity under the edge of the lead- ing pole-piece will be zero, when the magnetic difference of potential between this polar edge and the armature core, immediately beneath, is zero. The magnetic difference of po- tential across the gap at this point due to the field flux alone, will be the magnetic drop in the entrefer, or ($>d, where (B, is the field intensity in the gap with no current in the armature, Digitized by VjOOQ LC 1 88 ELECTRO-DYNAMIC MACHINERY. and d 9 the length of the entrefer in cms. The total M. M. of the armature, along the arc of one pole, will be — \ where wp is the number of turns covered by the pole, and t will be the total difference of potential in the magnetic circ of the armature. Assuming that the armature is not opera near the intensity of magnetic saturation, almost the enl reluctance in the armature circuit will be in the entrei Fig. 156 represents diagrammatically the magnetic circuit a Gramme-ring armature. The reluctance between be and in the field pole, also between ef and fa y in the armature, 1 be comparatively small, so that the total magnetic differei of potential developed by the armature will be expended in two air-gaps ab and de, half the M. M. F. of the turns bene the pole face being expended in each air-gap. Strictly spe FIG. 156. — MAGNETIC CIRCUITS OF GRAMME-RING ARMATURE DUE TO I OWN M. M. F. ing, the magnetic flux produced by the armature will not confined to the paths indicated by the dotted arrows, but ^ pass across the air-gap at all points not situated on the neui line cf. The above principles may be relied upon, howe\ to a first approximation. 211. In order, therefore, that a smooth-core armat should be capable of sparkless commutation, the M. M. of the turns on its surface, covered by each pole, should somewhat less than the drop of magnetic potential in e; air-gap, so as to leave a residual flux from the field in which reverse the armature current in the coil under commutati For example, if each air-gap or entrefer has a length o cms., and the intensity in the air is 3,000 gausses, the drop potential in the air will be 6,000 gilberts. If the numbei Digitized by VjOOQ IC ARMATURE REACTION. 189 Gramme-ring armature turns, covered by one pole-piece, is 200, then a current of 80 amperes from the armature will repre- sent 40 aniperes on each side, and the M. M. F., produced by this current will be x 40 X 200 = 10,056 gilberts, and 10 half of this amount, or 5,028, being less than the drop of field flux in the gap, should leave a margin for sparkless commu- # tation. 212. Although the preceding rule enables the limit of current for sparkless commutation, on a smooth-core armature, to be predicted under the conditions described, yet it by no means follows that sparkless commutation must necessarily be obtained if the M. M. F. of the armature lies within this limit. If, for example, the number of commutator segments is very small, the inductance of each segment may be considerable, and a powerful flux intensity may be required to reverse the current under the brush in the presence of such inductance. No exact rules have yet been formulated for the determina- tion of the inductance in a coil with which a given current strength, speed of rotation, and field intensity, shall render sparkless commutation possible. 213. The methods in general use for the suppression of sparking may be classified as follows: (1.) Those which aim at the reduction of inductance in the commuted coils. (2. ) Those which aim at the reduction of the current strength passing through the coil during its short circuit by the brush, and, therefore, at the reduction of the current strength which must be reversed before the short circuit is over. (3.) Those which aim at the reduction of the armature reac- tion, so as to reduce its influence in weakening the field in- tensity in which the coil is commuted. 214. There are two methods for reducing the inductance of the armature coils. The first is to employ a great number of commutator seg- ments, thus decreasing the number of turns in each coil under commutation. It is evident that an indefinitely great number Digitized by VjOOQ IC S'l* '"tt. V ■ i # 190 ELECTRO-DYNAMIC MACHINERY. of commutator segments would absolutely prevent sparkin A great number of commutator segments is, however, boi troublesome and expensive, so that in practice a reasonab maximum cannot be exceeded. The second method for lessening the inductance of the arm ture coils differs from the preceding only in the method « connection. It consists in providing two separate windin; or sets of coils ; or, as it is sometimes called, in double-windh the armature. The two separate windings are insulated fro each other, but are connected to the commutator at alterna segments, so that the brush rests coincidently upon segmen that are connected with each winding. Each winding ther fore, furnishes half the current strength, and the effect of tl inductance in each coil is reduced. 215. When the brushes are not so shifted as to bring tl diameter of commutation into coincidence with, or even in a vance of, the neutral point, the coil under commutation will 1 situated in a magnetic flux in the wrong direction; i. at any temperature t° C, will be approximately, R = r (1 -f- 0.004 /). In other words, the re- sistance will rise by 0.4 per cent, per degree centigrade of temperature elevation above zero. The result is, that at high temperatures, the wasteful activity, as I*R, in the armature, increases, increasing thereby both the loss in the machine and the tendency to temperature elevation. 238. . The temperature of the armature must not exceed that at which any of the materials employed in its construction would be deleteriously affected; /. < : -. ■1" - i . surfaces are freely exposed to the air, or are partly sheltered from it. Usually, however, the surfaces of the field coils must afford 1 6 square centimetres, or about 2.5 square inches per watt of activity developed in them as /■-tfheat. If the field ^-; winding consists of many layers of fine wire, the temperature of the deep seated layers will be greater than that of the super- ficial layer ; but if, on the contrary, the layers be few, and the wire coarse, the difference of temperature in the winding will be inconsiderable. The elevation of temperature on the field magnets of a generator is usually not greater than 30° C. at full load. 241. In the case of the armature, the speed at which it revolves through the air greatly increases its capability for dissipating heat and reducing its temperature, so that a much greater surface thermal activity can be permitted in the arma- 1 . , i ' ture than in the field coils. The usual allowance for eddy cur- rents, load currents and hysteretic losses combined, is about — th watt per square centimetre; 1. *., 1 — watts per square inch of armature surface, including the surface on the sides of the afniature, but excluding its internal core surface ; or, about three times more activity per unit area than on the field mag- nets. In some specially ventilated armatures, in which the core discs are spaced and separated at intervals, to permit the circulation of air from the interior outward by centrifugal force, the dissipation of heat can be so far increased that two watts per square inch of armature surface have been rendered practic- able. Much depends, however, upon the shape and size of * the armature, as well as upon its peripheral speed, so that no exact rule can be laid down. IT, ,; M Digitized by VjOOQ IC CHAPTER XX. REGULATION OF DYNAMOS. 242. As has already been pointed out (Par. 16), all self-excit ing continuous-current generators may be wound in one o three ways ; namely, (1.) Series-wound. (2.) Shunt-wound. (3.) Compound-wound. 243. Fig. 164 represents diagrammatically the connection! between the field and armature of a series-wound generator FIG. 164. — DIAGRAM OF SERIES WINDING. It will be observed that the current in the main circuit passe through the field magnet windings. The M, M. F. of the fiel( coils, therefore, increases directly with the current strengtl through the circuit. So long as the iron in the magnetic cir cuit of the machine is far from being saturated, the flux througl the armature increases with the M. M. F., approximately, 11 direct proportion, and the E. M. F. of the armature, conse quently, increases nearly in proportion to the current strength As soon as the iron in the circuit approaches saturation, th< flux increases more slowly, and finally, the E. M. F. of th< armature is scarcely increased by any increase in the curren strength through the circuit. 244. Fig. 165 represents diagrammatically the connection between the field and armature of a shunt-wound generator * 206 Digitized by VjOOQ LC REGULATION OF DYNAMOS, 207 Here the field magnets are wound with fine wire and the windings are connected in parallel with the external circuit, instead of being connected in series with it. Consequently, if the pressure at the brushes be considered as uniform, the current strength passing through the magnet coils must, by Ohm's law, be uniform, independent of the current strength in the main circuit. Thus, if the pressure at the brushes be assumed constant, at, say 100 volts, and the resistance of the magnet coils be 50 ohms, then the current strength through the magnet coils will be two amperes, independently of the strength of current supplied to the main circuit. 245. Practically, however, owing to the drop of pressure in the armature as the load increases, and also on account of the FIG. 165.— DIAGRAM OF SHUNT WINDING. shifting of the brushes that may be necessary with the increase of load, the pressure at the" brushes diminishes, and the cur- rent strength through the field magnets diminishes in the same proportion. The tendency in a shunt-wound machine is, there- fore, to diminish its M. M. F., and its resulting E. M. F., as the load on the generator increases. In order to maintain a con- stant pressure at the brushes under all variations of load, it is necessary to adjust the strength of current passing through the field magnets, so that the M. M. F. at full load shall be slightly in excess of the M. M. F. at light load. This is usually accomplished by the insertion of a rheostat in the field magnet circuit, so that some or all of this resistance can be cut out by hand at full load, thereby increasing the current strength through the magnet coils. 246. If, for example, the full-load activity of the machine be io KW at 100 volts pressure, the full-load current strength Digitized by VjOOQ LC ...!'' h ft- '■. : -H 208 ELECTRO-DYNAMIC MACHINERY. will be 100 amperes. Assuming the resistance of the armatu to be 0.05 ohm, the drop of pressure in the armature at fi load will be 100 x 0.05 = 5 volts, and the additional drop pressure, owing to the shifting of the brushes in order avoid sparking, may be 2 volts more, making a total drc in pressure of 7 volts. The effect of this drop would 1 to reduce the current strength in the field magnet coils fro 2 amperes to — = 1.86 amperes, thus reducing both the fli through the armature and the E. M. F., so that a balan< between the E. M. F. and its excitation might be found a say, 90 volts, if no means were adopted to regulate the cu rent strength through the field coils. In other words, tl FIG. 166. — DIAGRAM OF COMPOUND WINDING. pressure at the brushes would vary by 10 volts between Kg and full load. 247. Fig. 166 represents the connections between the fie and armature of a compound-wound generator. Here tl principal M. M. F. furnished by the magnet coils is that di to the shunt coil, composed of many turns of fine wire, i auxiliary series coil, of comparatively few turns of coarse wir being also employed in the main circuit. As the load increase the M. M. F. generated by the shunt winding tends to diminij as above described, but the M. M. F. due to the series cc increases. By suitably proportioning these two opposi influences, the M. M. F. may be automatically so controlle that the pressure at the brushes shall remain constant, "eith at the brushes of the generator, or at the terminals of tl motor or other translating device, which may be situated at considerable distance from the generator. In order to effe this latter result, the M. M. F. of the series coil must compe Digitized by VjOOQ LC kk REGULATION OF DYNAMOS. S09 sate not only for the drop in the armature, but also for the drop in the conductors leading from the generator to the motor, so that these external conductors may be regarded, electrically, as forming an extension of the armature winding, and, in this sense, the generator delivers a constant pressure at its final terminals on the motor. Such a machine is said to be over compounded. 248. Series-wound generators are almost invariably employed for series-arc lighting, since it would be very difficult to supply the required M. M. F. for their magnets by a shunt winding, considering that the pressure at the brushes varies between such wide limits; and, even if such shunt winding could be supplied, it would necessarily be formed of a very long and fine wire, and, consequently, would become troublesome and expensive. Series arc-lighting generators are sometimes constructed for as many as 200 lights, representing about 10,000 volts at the generator terminals at full load, and a shunt winding for such a pressure would be very expensive. 249. Shunt-wound generators are usually employed for sup- plying incandescent lighting from a central station, and their pressure is varied by hand regulation. Compound-wound generators are usually employed for sup- plying motors from central stations, and also for incandescent lights and motors in isolated plants. 250. In the design and use of generators, it is important to know how the E. M. F. generated in the armature at a given speed varies with the current passing through the field magnets. We have seen that so long as the brushes remained unaltered in position, the E. M. F. in the armature, in C. G. S. units, is equal to the product of the number of turns on the armature, the number of useful webers passing through the armature from each pole, and the number of revolutions per second. Consequently, the E. M. F. of such an armature, running at a constant speed, depends .directly upon the flux through its magnetic circuit or circuits. If we vary the current strength through the field magnets, and, consequently, the M. M. F., we can observe the pressure in volts, which the Digitized by VjOOQ LC 2IO ELECTRO-DYNAMIC MACHINERY. machine will deliver at its brushes at light load. A serie of such observations, plotted in a curve, gives what is calle< the characteristic curve of the generator. In the case o a self-exciting, series-wound generator, it is only possible t< FIG. I67. — CURVE OF E. M. F. DEVELOPED IN THE ARMATURE OF A SERIES WOUND DYNAMO, WITH REFERENCE TO CURRENT STRENGTH IN A CIRCUIT. vary the M. M. F. by varying the load, and, consequently, b] including, in the pressure at the brushes, the drop taking placi in the armature. The curve obtained from a series-wounc machine under such circumstances, is called an external char acteristic, and the internal characteristic may be determined fron it by correcting for the drop in the armature. Digitized by VjOOQ IC REGULATION OF DYNAMOS. 211 251. Fig. 167 represents the internal and external charac- teristics of a particular series-wound generator intended to supply a maximum of 70 amperes at 50 volts terminal pressure or 3,500 watts. The pressure at terminals, when the load was varied so as to produce the required variations of current strength through the magnets, followed the broken line A B C, which is, there- fore, the external characteristic of the machine. If we add to the ordinates of this line from point to point, the drop of pres- sure in the armature at the corresponding current strength, the full line o D E F, is obtained, which is, therefore, the internal characteristic of the generator or the curve of its E. M. F. in relation to the exciting current in its field coils. The useful E. M. F. developed by the armature may be expressed by the formula, E = - =. volts. so that, if two observations are secured, the whole internal characteristic curve may be deduced to a very fair degree of accuracy. For example, in Fig. 167, the E." M. F. at 20 amperes = 74 volts, and at 70 amperes, 95 volts. From these observations we may take the two equations, 20 _ 70 74 = — ; and 95 = x + 20 y x 4- 70 _y From these two equations we obtain x = 0.0836 and y = 0.00933, so that the E. M. F. at any current strength through the field magnets is E = — - , ■ 7 - T volts. 0.0836 + 0.00933/ The dotted curve o HE F, which lies close to the full curve o D E F, represents the locus of this equation. It will be observed that the dotted line practically coincides with the full line representing the observations, except within the first 20 amperes of magnetizing current strength. 252. Fig. 168 represents the characteristic curve of a shunt- wound generator, of 200 KW capacity. Here the current strength through the field magnets was not observed, but the pressure acting on the field coils was noted. Assuming, as would probably be very nearly true, that the resistance of the Digitized by VjOOQ IC : *«. 212 ELECTRO-DYNAMIC MACHINERY. field magnet coils remained constant throughout the observa tions, the exciting current strength would be proportional t the pressure acting on the coils. With 40 volts on the magnets the E. M. F. at the brushes with the external circuit broke was 71 volts, and increased, as shown by the full line A B C, t 190 I7Q m / > f 1 vo b 9 9 DN FJ 4 ELD t I 7 8 9 jJ » u L0 IS 90 12 to ll FIG. 168. — CHARACTERISTIC CURVE OF SHUNT-WOUND DYNAMO. 185 volts, with 140 volts on the magnets. Here also th E. M. F., 2£, may be expressed by the Frolich equatior E = — — , e being the pressure on the field magnets; takin the two observations, 120 = — 1 and 174 = — : , w x + 7° y x + I2 ° j find x = 0.43 and y = 0.0022, from which the general equatio becomes, ^ e E = O.43 + 0.0022 € volts. Digitized by VjOOQ LC REGULA TION OF D YATAMOS. ? I $ The locus of this equation is represented by the dotted line, which practically coincides with the full line A B C, of observation. 253. When, therefore, two reliable observations have been made of the E. M. F. generated by an armature, at observed exciting currejit strengths, or pressures, situated not too closely together, it is possible to construct the characteristic curve throughout to a degree of accuracy sufficient for all practical purposes. The Frolich equation, by which this is possible, is a con- sequence of the fact that the reluctance of the air paths in the magnetic circuit of a generator is. constant, while the reluc- tivity of the iron in the circuit is everywhere capable of being expressed by the formula v = a + b 3C (Par. 59) ; and, consequently, the total apparent reluctance of the armature takes the form x -\-y$ y and the useful flux passing through the armature # = , SF, being the magnetomo- tive force in gilberts, but SF, may be expressed in ampere- turns, in amperes or in volts applied to the coils. 254. When the characteristic curves of a shunt machine have been obtained, it is a simple matter to determine what the series winding must be in order to properly compound it, ' either for the drop in the armature, or for the drop in any given portion of the external circuit as well. Thus, suppose it be required to determine the series winding for the machine whose characteristic curve is represented in Fig. 168. If the E. M. F. required at the terminals of the machine be 120 volts at all loads, and if the drop in the armature, due to its resistance at full load, as well as the resistance of its series coil, and to any shifting of the brushes that may be necessary, amounts in all to 10 volts, then the full-load current must supply the M. M. F. necessary to carry the E. M. F. from 120 to 130 volts, equivalent to raising the pressure by 8 volts from, 70 to 78 volts on the shunt winding. The increase in current strength from the shunt winding represented by these eight volts multiplied by the number of turns in the shunt winding, gives the M. M. F. required, and the full-load current must Digitized by VjOOQ IC 214 ELECTRO-DYNAMIC MACHINERY. pass through a sufficient number of turns to supply ti M. M. F. in its series coil. 255. In all commercial circuits, electro-receptive devk require to be operated either at constant current or at consta pressure. The majority of such devices are designed for cc stant pressure; such, for example, are parallel or multip connected incandescent lamps and motors. Some devic however, require to be operated by a constant current. ' these, the arc lamp is, perhaps, the most important. Seri FIG. I69. — SHUNT FIELD \ND RHEOSTAT. connected incandescent lamps, and a few forms of motors, al belong to this class. 256. In order to maintain a constant pressure at the t minals of a motor with a varying load, it is necessary, order to compensate for the drop of pressure in supply cc ductors, that the pressure at the generator terminals either kept constant, or slightly raised as the load increases. W shunt-wound machines this regulation requires to be carri out by hand, a rheostat being inserted between the field a the armature, as shown in Fig. 169. 257. Various forms are given to rheostats for such purpos They consist, however, essentially of coils of wire, usually ir wire, so arranged as to expose a sufficiently large surface the surrounding air, as to enable them to keep within sj limits of temperature under all conditions of use. The resi ance is divided into a number of separate coils and the t minals of these are connected to brass plates usually arran§ Digitized by VjOOQ IC REGULATION OF DYNAMOS. 2'S in circles, upon the external surface of a plate of slate, wood or other non-conducting material, so that, by the aid of a handle, a contact strip can be brought into connection with any one of them. The coils being arranged in series, the movement of the handle in one direction adds resistance to the field circuit, and in the opposite direction, cuts resistance out FIGS. I70 AND 171. — FORMS OF FIELD RHEOSTAT. of the circuit. Figs. 170 and 171 show different forms of field rheostats, with wheel controlling handles. In some rheostats the resistance wire is embedded in an enamel, which is caused to adhere to a plate of cast iron. This gives a very compact form of resistance ; for, the intimate contact of the wire with the iron plate, together with the large free surface of the plate, enables the heat to be readily dissipated and prevents any great elevation of temperature from being attained. Two of such rheostats are shown in Fig. 172. 258. Compound-wound machines can be made to regulate automatically, and do not require to have their E. M. F. Digitized by VjOOQ IC 2l6 ELECTRO-DYNAMIC MACHINERY. adjusted by the aid of a field rheostat. For this reason the are very extensively used in the operation of electric motors. Series-wound machines are invariably used for operating ar lamps in series. Since the load they have to maintain is ap to be variable, such machines must possess the power of var} ing their E. M. F. within wide limits. Two methods are in us for maintaining constant the strength of current. That in mo« general use is to shift the position of the collecting brushes o the commutator so as to take off a higher or lower E. M. I according as the load in the external circuit increases or d( creases. The effect of this shifting will be evident from a inspection of Fig. 156 ; for, if the diameter of commutation b FIG. 172. — ENAMEL RHEOSTATS. shifted to the right or left, the E. M. F. in some of the coi will be opposed to that in the remainder, the difference on! being delivered at the brushes. In practice, the diameter < commutation would never reach the position of maximum I M. F. represented in Fig. 156, and might, on the other hanc rotate through a sufficiently large angle to produce only a sma fraction of the total E. M. F. < 259. In all cases where the brushes are shifted through considerable range over the commutator, care has to be take to avoid the sparking that is likely to ensue if a certain balanc is not maintained between the M. M. F. of the armature an the magnetic intensity in the air-gap. The fact that the currer strength through the armature coils is practically constant « Digitized by VjOOQ LC REGULATION OF DYNAMOS. 217 all loads, enables this balance to be effectually maintained, when once it has been reached at any load. FIG. 173. — OPEN COIL- WINDING. mon or neutral point 0. In the position represented, the coil A, is disconnected from the circuits, the coils B and C, remain- ing in the circuit of the brushes b b\ 261. In closed-coil, series-wound, arc-light generators, the brushes are given a forward lead ; i. e. 9 a lead in the direction of the rotation of the armature. The amount of this lead controls the E. M. F. produced between the brushes. It is essential, in order to prevent violent sparking, that the coil under commuta- tion should be running through an intensity sufficient to nearly reverse the current in the commuted coil during the time of its short circuiting. Since the current strength in the field, and also in the armature, is maintained constant at all loads, it is necessary that the intensity of flux, through which the com- muted coils run, should be uniform, or nearly uniform, at all loads and of the proper degree to effect current reversal. The 18 *• ' " & * • 260. Series-wound arc-light generators have their armatures wound in two ways ; namely, closed-coi{ armatures, and open-coil j£ • " |! armatures. In the former, all the armature coils are constantly £ : in the circuit, while in the latter, some of the coils are cut out of the circuit by the commutator, during a portion of the revo- lution. The ordinary continuous-current generator for pro- ducing constant pressure is, therefore, a closed -coil armature. Fig. 173 represents diagram matically a form of open-coil arma- ture winding. The three coils shown are ooanected to a corn- Digitized by VjOOQ IC 2l8 ELECTRO-DYNAMIC MACHINERY. M. M. F. of the field magnet, is constant and the M. M F. of tl armature is also constant, but the flux produced by the M. \ F. of the armature varies with the position of the brushes ar the number of active turns that exist in that portion of the arm ture which is covered by the pole-piece, on each side of the diar eter of commutation. The pole-pieces are usually so shap* that as the number of active turns in the armature covered t each pole increase ; /. AXJ£L£L. 22$ armature in the second, and a current will pass through the second armature in a direction opposite to that which it tends to produce, and, therefore, in a direction tending to rotate the second generator as a motor. In other words, the control of pressure between the two machines must be within closer limits than two per cent. Early in the history of central station practice, difficulties were experienced in controlling the pressure of multiple-connected dynamos within limits nec- essary to avoid this unequalizing action, but at the present time, the governing of the engines and the control of the field magnets are so reliable, that this difficulty has practically dis- appeared. It is important to remember, however, that the larger the generator unit employed, and the smaller the drop in pressure taking place at full load through its armature, the narrower is the limit of speed or regulation, in which inde- pendent units will equalize their load, although as a counter- acting tendency, the larger will be the amount of power which, in case of disequalizing, will be thrown upon the leading ma- chine tending to check its acceleration. 271. Compound-wound generators are almost invariably em- ployed for supplying electric currents to street railway sys- tems. This is principally for the reason that the load in a street railway system is necessarily liable to sudden and marked fluctuations, and these fluctuations would be liable to produce marked variations in the pressure at the generator terminals, if the machines were merely shunt wound. Such generators are operated in parallel units. Here, as in the case of shunt- wound machines, it is necessary that the E. M. F. generated by each machine should be nearly the same, in order that the load should be equally distributed ; but instability of control is greater in the case of compound-wound machines than in the case of shunt machines, for the reason that when one of a number of parallel-connected shunt- wound machines acceler- ates, and thereby rises in E. M. F., so as to assume an undue share of the load, the drop in the armature thereby increases, and tends to diminish the irregularity, so that not only does the greater load tend to retard the engine connected to the leading machine, but also the drop in its armature aids in equalizing the distribution. Digitized by VjOOQ IC 2 24 ELECTRO-D YNAMIC MA CHIN EH V. In the case of compound-wound machines in parallel, any acceleration tends, as before, to increase the E. M. F. of the generator and, therefore, its share of the load, but the series coil of the compound winding being excited by the additional load, tends to increase the output of the machine, and, there- fore, the governing of the engine has to be entirely depended on to prevent disequalization. Of recent years, however, the plan has been widely adopted of employing an equalizing bar between compound-wound generating units operated in par- R° A S f t * t 1 t t + 1- V& i FIG. I75.— PARALLEL CONNECTION OF COMPOUND : WOUND GENERATORS. allel. The connections of an equalizing bar are shown in Fig. 175. Here the two compound-wound generators are connected to the positive and negative omnibus bars, or bus bars, as they are generally termed, AA and BB, while the series coils are connected together in parallel by the equalizing bar QQ. It is evident that the equalizing bar connects all' series coils of the different dynamos in parallel, so that any excess of current, supplied by the armature. of one machine, must necessarily ex- cite all the generators to the same extent. • 272. When a number of compound-wound generators are running in parallel, and the load increases, so that it is desired to add another unit to the generating battery of dynamos, the engine connected with the new unit is brought up to speed, and the shunt field excited* This brings the E. M/. F. of the Digitized by VjOOQ IC DYNAMOS IN SERIES OR IN PARALLEL. 225 machine up to nearly 500 volts. Its series winding is then connected in parallel with the series winding of the neighbor- ing machines, by the switch on the equalizing bar, so that its excitation is then equal to that of all the other machines. The £. M. F. of the machine is then brought up slightly in excess of the station pressure by the aid of the field rheostat, and, as soon as this is accomplished, the main armature switch is closed, thus connecting the armature with the bus bars. The load of the machine is finally adjusted by increasing the shunt excita- tion, with the aid of the rheostat, until the ammeter connected with the machine shows that its load is approximately equal to that of the neighboring generators. The same steps are taken in reverse order to remove a generator from the circuit. 273. Fig. 176 is a diagram of a street-railway switchboard for two generators. It is customary, both for convenience and simplicity, to erect switchboards in panels, one for each generating unit, so that each panel controls a separate unit, and is in immediate connection with its neighbors. In the figure, the two panels are designated by dotted lines, the one on the left, active, and the one on the right, out of use. On each panel there are two main switches, P and N, for the posi- tive and negative armature terminals. A smaller switch, not shown, is usually located on the right of each panel, and is for lighting up the station lamps from any panel and its connected machines, at will. R 9 is a shunt rheostat, placed at the back of the panel, with its handle extending through to the front, and S, is a small switch for opening and closing the shunt circuit of the field coils through the rheostat, R. A, is the generator ammeter, brought into use by the switches P and JV y and T 9 is the automatic circuit-breaker for the panel. This electro- magnetic circuit-breaker, opens the circuit of the machine when the current strength, owing to a short circuit or other abnormal condition, becomes dangerously great, thereby reliev- ing the generator of the strain. The switch connected to the equalizing bar E is not placed in this instance, on the panel, but is mounted close to the generator with the object of diminishing the amount of copper conductor required. Each panel is also provided with a voltmeter connection and lightning arrester, which have been omitted here for the sake of simplicity. Digitized by VjOOQ IC 226 ELECTRO-DYNAMIC MACHINERY. 274. The operations for introducing a unit into the batter] of generators in this case, is as follows : the generator is brought up to speed, the equalizing switch is closed, % thus connecting the series coils of the machines in parallel with the machine: in use. The positive main switch JP 9 is next closed, connecting FIG. I76. — DIAGRAM OF SWITCHBOARD CONNECTIONS FOR TWO COMPOUND- WOUND GENERATORS. one side of the armature to ground and to return track feeders The field switch S, is next closed, and the E. M. F. of th< machine brought up to slightly above station pressure by th< aid of the rheostat R ; finally, the negative main switch N, \\ closed, throwing the armature into the battery, and the load u Digitized by VjOOQ IC DYNAMOS IN SERIES OR /AT PARALLEL. 227 adjusted by the rheostat R, in accordance with the indications of the ammeter A. 275. Another arrangement for railway switchboards consists in mounting the three switches, in close proximity to each other and attaching a single handle to the three blades, so that the three connections may be made or broken by a single operation. When the railway mains are connected with the station by several feeders, it is customary to add another section to the switchboard where switches and ammeters are provided for handling the various feeders. ■■■.U.f: :•!':%;; Digitized by VjOOQ IC CHAPTER XXII. DISC ARMATURES AND SINGLE-FIELD-COIL MACHINES. 276. Before leaving the subject of generators, it may be we to discuss a few types of generators that do not fall under tl FIG. I77. — DISC- ARMATURE GENERATOR. types already discussed, and which are occasionally met wi in practice. These may be described as ; (1.) Disc-armature machines. (2.) Single-field-coil machines. 238 Digitized by VjOOQ IC §, FIG. I78. — DISC ARMATURE. iWU, \'- !■$■■: Digitized by VjOOQ IC 230 ELECTRO-DYNAMIC MACHINERY. (3.) Unipolar machines, or commutatorless continues current machines. 277. Generators employing disc armatures are frequen used in Europe, and although they are very seldom employ in the United States, yet it is proper to describe them as bei types of machines capable of efficient use. In one form disc-armature generator, the armature is devoid of iron, and built of conducting spokes like a wheel, which revolves ii vertical plane between opposite field-magnet poles. Suet FIG. I79. — DIAGRAM OF DISC- ARMATURE WINDING. disc-armature machine is shown in Fig. 177. It is to observed that the entire machine is practically encased in ir and is provided with three windows on the vertical fa through these windows the brushes, ££, rest on the comr tator which is placed on the periphery of the disc, resembl in this respect the generator in Fig. 103. The armature oft machine is shown in Fig. 178 mounted on a suitable suppc The radial spokes are of soft iron, and are connected into lo< by the copper strips leading to the commutator segments the periphery. The object of employing iron spokes is diminish the reluctance of the air-gap. The field poles f; w Digitized by VjOOQ IC DISC ARM A TURES. *3* each other, being separated by the disc armature, which revolves between them. Such an armature is evidently capa- ble of being operated at an abnormally high temperature without danger, being constructed of practically fireproof materials. The electric connections of an octopolar machine are represented diagrammatically in Fig. 179. The brushes, it will be observed, are applied at the centres of any adjacent FIG. 180. — DISC-ARMATURE GENERATOR. pair of poles. Another form of the machine is represented in Fig. 180. 278. An example of a single-field-coil multipolar dynamo is shown in Fig. 181. This is a quadripolar generator with four sets of brushes. The interior of the field frame, with its pro- jecting pole-pieces and exciting coil, is shown in Fig. 182. It will be seen that the field frame is made in halves, Digitized by VjOOQ IC FIG. l8l. — COMPOUND-WOUND GENERATOR "WITH SINGLE FIELD COIL. FIG. 182. — DETAILS OF MAGNET, SINGLE-FIELD-COIL GENERATOR. Digitized by VjOOQ IC SINGLE-FIELDCOIL MACHINES.- *33 between which are enclosed the armature and the single field magnetizing coil. Four projections JV 9 N, and S, S, form the pole-pieces of the quadripolar field ; that is to say, the magnetic FIG. I83. — ARMATURE OF QUADRIPOLAR, SINGLE-FIELD-COIL MACHINE. flux produced by the M. M. F. of the. single coil C C, passes through the field frame into the two pole faces N and N 9 in parallel through the armature into the adjacent pole faces S, S 9 thus completing the circuit through the field frame. The drum-wound, toothed-core armature, is shown in Fig. 183. Digitized by VjOOQ IC CHAPTER XXIII. COMMUTATORLESS CONTINUOUS-CURRENT GENERATORS. 279. Commutatorless continuous-current dynamos are sometime called unipolar dynamos, although erroneously. It is impossibi to produce a single magnetic pole in a magnet, # since all maj netic flux is necessarily circuital, and must produce poles, bot where it enters and where it leaves a magnet. The fact the these machines are capable of furnishing a continuous currer without the aid of a commutator, at one time caused considei able study to be given to them in the hope of rendering thei FIG. 184. — FARADAY DISC. commercially practicable. The maximum E. M. F. which the have been constructed to produce, appears, however, to hav been about six volts, and, consequently, they have practicall fallen out of use, although they have been commerciall employed for electroplating. 280. Fig. 184 represents what is known as a Faraday disi This was, in fact, the earliest dynamo ever produced, and wa of the so-called unipolar type; for here, a copper disc L rotated, by mechanical force, about an axis parallel to th direction of the magnetic flux, supplied by a permanent horse shoe magnet MM, continuously cuts magnetic flux in the sam Digitized by VjOOQ IC CONTINUOUS-CURRENT GENERATORS. *35 direction, and, consequently, furnishes a continuous E. M. F. between the terminals S, S\ without the use of a commutator. 281. The portion of the disc lying between the poles is caused to rotate in a nearly uniform magnetic flux, and with a velocity which depends upon the radius of the disc at the point con- sidered, as well as on the angular speed of rotation. The di- rection of the E. M. F. induced will be radially downward from the axis to the periphery, and, if connection be secured between the axis as one terminal, and the rotating contact or brush as the' other terminal, an E. M. F. will be continuously produced in that portion of the disc which lies beneath the poles; or, more strictly, in that portion of the disc which passes through the flux between them and around their edges. If, however, as in Fig. 185, the disc be completely covered by the pole faces, a FIG. 185. — FARADAY DISC. radial system of E. M. Fs. will be induced outward in the direc- tions indicated by the arrows, or inward, if the direction of rotation be reversed. If no contacts are applied to the disc, these E. M. Fs. will supply no current, and will do no work. If brushes are applied at the axis, and at any or all parts of the periphery, the E. M. F. can be led off to the external circuit. 282. The value of the E. M. F. will depend upon the angular speed of rotation, the intensity of the magnetic flux, and the radius of the disc. The intensity of the magnetic flux can usually be made much greater by the use of a soft-iron disc instead of a copper disc, thereby practically reducing the reluctance of the magnetic circuit between the poles to that of two clearance films of air, since the reluctance of the iron disc will be negligibly small. 283. If we consider any small length of radius d /, Fig. 186, situated .at a distance /, from the axis. of the disc, the E. M. F. Digitized by VjOOQ IC 236 ELECTRO-DYNAMIC MACHINERY. generated in this element of the disc will be the product of t intensity, the length of the element, and its velocity across t flux. The element will be moving across the magnetic flux uniform intensity, (fc gausses, at a velocity / go centimetres p second, where go, is the angular velocity of the disc in radia per second. Consequently, the E. M. F. in this element will t de = / co . dr . B C. G. S. units of E. M. F. The total E. M. F. will be the sum of the elementary E. M. ] included in the radius taken from / = o, to / = Z, the radi of the disc, or the integral of de 9 in the above equation betwc the limits / = o> and / = Z. This integral is — go (B = The E. M. F. from such a disc, therefore, increases as 1 fig. 186 square of the radius of the disc, directly as the speed, a directly as the uniform intensity of the magnetic flux. T same result can be obtained in a slightly different expressic since go = 2 n n y where «, is the number of revolutions of 1 Z* disc in a second, e = — . 27T«(fc = 7rZ*«(B = .S«(fc wh< 2 S, is the active surface of the disc. This will also be tru< the surface S, instead of extending over the entire face of t disc, extends only from the periphery to some intermedi radius. From this point of view the E. M. F. of the disc equal to the product of the intensity in which it runs, 1 number of revolutions it makes per secondhand its active s face in square centimetres. To reduce this E. M. F. to vol we have to divide by 100,000,000. 284. There are two recognized types of commutatorl continuous-current dynamos; namely, the disc type and cylinder type. The outlines of a particular form of the disc t] are represented in Fig. 187. Here the shaft S S, usually h< •Bigiti CONTINUOUS-CURRENT GENERATORS. m zontal, carries a concentric, perpendicular disc of copper or iron, rotating in a vertical plane, in the ring-shaped magnetic frame, in a circular groove, through the flux produced by two <:oils of wire. The general direction of the magnetic flux, through the field frame and disc, is represented by the curved arrows. It will be observed that the magnetic flux will be uniformly distributed so as to pass through the rotating disc at right angles. Brushes rest on the periphery, and on the shaft, of the disc. Inasmuch as the E. M. F. in the disc is radially directed at all points, the brushes for carrying off the current may be as numerous as is desired. These brushes are TIG. 187. — DISC TYPE OF COMMUTATORLESS DIRECT-CURRENT GENERATOR. marked £, b, in the figure. A and B 9 are the main terminals of the machine, and/, /', the field terminals. 285. If we suppose that the intensity (B, is 12,000 gausses, that the radius of the disc is 1 foot, or 30.48 centimetres, that the active surface on each side of the disc is 2,500 square cen- timetres, and that the speed of rotation is 2,400 revolutions per minute, or 40 revolutions per second, then the E. M. F. obtain- able from the machine will be : 2,500 x 40 x 12,000 = I2 o volts 100,000,000 In order to produce an E. M. F. of say 140 volts, such as would be required for continuous-current central-station gen- Digitized by VjOOQ IC 238 ELECTRO-DYNAMIC MACHINERY. erators, it would be necessary either to connect a number < such machines in series, or to increase the diameter of the dis or to increase the speed of rotation. It would, probably, t unsafe to run the disc at a peripheral speed exceeding 200 mill per hour, owing to the dangerously powerful ' mechanic stresses that would be developed in it by centrifugal fore This important mechanical consideration imposes a limit < speed of rotation and diameter of the disc, taken conjoint! By increasing, however, the active surface of the disc, and, \ the same time, working at a safe peripheral velocity, it wou FIG. 188. — DIAGRAM SHOWING FLUX DENSITY THROUGH DISC ALONG A RADIUS. be possible to construct large disc generators of this type f< an E. M. F. of 100 or 150 volts. 286. It should be borne in mind that although such machini would be capable of producing continuous currents without tl use of a commutator, yet the necessity of maintaining efficiei rubbing contacts on the periphery of the rapidly-revolving di introduces a difficulty and waste of power which has hither prevented the development of this system, and, probabl accounts for the fact that large machines of this type do n exist. 287. Irregularities in the distribution of magnetic flux ov the surface of the disc may give rise to strong eddy curren and waste of power in the same. If the flux be variable aloi any radius of the disc O B, as represented in Fig. 188, so th the intensity (B, is not uniform along these lines, this irreg larity will not produce eddy currents in the disc unless the di tribution is different along different radii. In other words, Digitized by VjOOQ IC CONTINUOUS-CURRENT GENERA TORS, *39 the distribution of magnetic flux and intensity are symmetrical about the axis of rotation of the disc, the irregularities which exist will only alter the intensity of E. M. F. in different elements of a radius. In Fig. 188, the intensity, instead of being uniform from centre to edge, as indicated by the straight line d a c, increases toward the edge, following the line a b+ PIG. 189. — CYLINDER TYPE OF COMMUTATORLESS CONTINUOUS-CURRENT GENERATOR. The formula for determining the £. M. F. of the disc is in such case rendered somewhat more complex. 288. If, however, the curve a b> of flux intensity along different radii is different, so that the distribution of magnetic intensity is not symmetrical about the axis of rotation, then eddy currents will tend to form, the amount of power so wasted depending upon the amount of irregularity, the resis- tivity of the material in the disc, and the load on the machine. \M FIG. 190. — INDICATING DIRECTION OF E. M. F. INDUCED IN REVOLVING CYLINDER. 289. Fig. 189 represents the outlines of a particular form of the. second, or cylindrical type of commutatorless continuous- current generator. Here a metallic conducting cylinder cccc, revolves concentrically upon the shaft S S, through the uniform magnetic flux, produced by the field frame surrounding it. Here, however, two sets of brushes bb y b'b\ have to be applied to the edges of the cylinder in order to supply the main ter- Digitized by VjOOQ IC 240 ELECTRO-DYNAMIC MACHINERY. mmals A and B. The terminals of the four circular coils con- stituting the field winding are shown at/, /'. 290. If the magnetic intensity produced by the field is uniform, the E. M. F. will be generated in lines along the sur- face of the cylinder parallel to its axis, as represented in Fig. 190. If v, be the peripheral velocity of the cylinder in centi- metres per second, /, the length of the cylinder in centimetres, and (R the uniform intensity, in gausses, the E. M. F. generated by the machine will be : v I <$> . • e = volts. 100,000,000 Machines of the cylindrical type have been constructed and used for electrolytic apparatus, and give very powerful cur- rents, as compared with ordinary generators of the same dimensions employing commutators. Unsatisfactory as these unipolar machines have so far proved, except in special cases, they are, nevertheless, the only dynamos which have yet been successfully constructed for furnishing continuous currents without the use of a commutator. Digitized by VjOOQ IC CHAPTER XXIV. ELECTRO-DYNAMIC FORCE. 291. In discussing the magnetic flux surrounding an active conductor, we have observed in Par. 34, that it is distributed in concentric cylinders around the conductor, as shown in Figs. 27 and 28. It is evident that if a straight conducting FIG. 191.— STRAIGHT CONDUCTOR IN UNIFORM MAGNETIC FLUX. wire A B, say / cms. in length, as shown in Fig. 191, be situated in the uniform magnetic flux represented by the arrows, the flux will exert no mechanical influence upon the wire. If, how- ever, the wire carries a uniform current in the direction from FIG. I92. — MAGNETIC FLUX SURROUNDING ACTIVE CONDUCTOR. A to 2?, then, as is represented diagrammatically in Fig. 192, the system of concentric circular flux, indicated by a single circle of arrows, will be established around the wire, appearing clockwise to an observer looking from A 9 along the direction in which the current flows, and, as has already been pointed out, this circular magnetic flux will have an intensity propor- tional to the current strength. Digitized by VjOOQ LC 242 ELECTRO-DYNAMIC MACHINERY. 292. If such a conductor be introduced into a uniform mag- netic flux, as is represented in Fig. 193, it is evident that above the wire at C, the direction of the flux produced by the current is the same as that of the field, while below the wire at D, the direction of the flux from the current is opposite to that from the field. Consequently, the flux above the wire is denser, FIG. I93. — DIAGRAM SHOWING DIRECTION IN ELECTRO-DYNAMIC FORCE. and that below the wire is weaker, or less dense, than that of the rest of the field. The effect of this dissymmetrical distri- bution of the flux density in the immediate neighborhood of the wire, is to produce a mechanical force exerted upon the substance of the wire, called the electro-dynamic force, tending to move it from the region of densest flux toward the region of weakest flux; or, in the case of Fig. 193, vertically down- FIG. I94. — DIAGRAM SHOWING DIRECTION IN ELECTRO-DYNAMIC FORCE. ward, as indicated by the large arrow. If, however, the direc- tion of the current in the wire be reversed, as shown in Fig. 194, and that of the external field remain unchanged, the flux will be densest beneath the wire and weakest above it, so that the electro-dynamic force will now be exerted in the opposite direction, or vertically upward, as shown by the large arrows. Digitized by VjOOQ IC ELECTRO-DYNAMIC FORCE. 243 293. If the direction both of the current in the wire and the flux in the external field be reversed, the direction of the electro-dynamic force will not be changed, as is represented in Fig. 195, where the direction of the electro-dynamic force is downward as in Fig. 193, though the direction of the current and the direction of the magnetic field are both reversed. 294. A convenient rule for remembering the direction of the motion is known as Fleming's hand rule. It is, in gen- eral, the same as that already given for dynamos in Par. 81, except that in applying it, the left hand must be used instead of the right. For example, if the hand be held as in the rule for dynamos, if the/orefinger of the left hand shows the direc- tion of the/lux, and the middle finger the direction of the cur- FIG. I95. — DIAGRAM SHOWING DIRECTION IN ELECTRO-DYNAMIC FORCE. rent, then the thumb will show the direction of the motion. It must be remembered, that in applying Fleming's rule, the right hand is used for dynamos in determining the direction of the induced E. M. F.,and the left hand for motors in deter- mining the direction of motion. 295. We shall now determine the value of the electro- dynamic force in any given case, on the doctrine of the con- servation of energy. To do this, we may consider the ideal apparatus, represented in Fig. 196, where a horizontal con- ductor EF, moves without friction against two vertical metallic uprights A £, and C D. This conductor is supported by a weightless thread, passing over two frictionless pulleys F, F, and bearing a weight W. If now a current enters the upright A B y and, passing through the sliding conductor E F, leaves the Digitized by VjOOQ LC 244 ELECTRO-DYNAMIC MACHINERY. upright CD, at C, then, in accordance with the preceding principles, under the influence of the uniform magnetic flux passing horizontally across the bar in the direction of the arrows, an electro-dynamic force will act vertically downwards upon the rod. If this electro-dynamic force is sufficiently powerful to raise the weight W, it will evidently do work on such weight, as soon as it causes the bar to move. Let us suppose that it produces a steady velocity of the bar E F y oiv cms. per second, in a downward direction. Then ft/, be the FIG. I96. — IDEAL ELECTRO-DYNAMIC MOTOR. electro-dynamic force in dynes exerted on the bar, the activity exerted will be, vf centimetre-dynes-per-second, or ergs-per- second. Since 10,000,000 ergs make one joule, this will be an activity of vf 10,000,000 joules-per-second, or watts. This activity will be expended in raising the weight JV, assuming the absence of friction. As in all cases of work expended, the requisite activity to perform such work must be drawn from some source, and in this case the source is the electric circuit. 296. When the bar of length / cms. moves with the velocity of v centimetres-per-second, through the uniform flux of den- Digitized by VjOOQ LC r > i ELECTRO-DYNAMIC FORCE. 245 sity (B, it must generate an £. M. F. as stated in Par. 82, of e = (fc / v 9 C. G. S. units, or f &iv . i = volts. j- 100,000,000 I This E. M. F. is always directed against the current in the J wire, and is, therefore, always a C. E. M. F. in the circuit [ The current of i amperes passing through the rod will, there* [ fore, do work upon this C. E. M. F. with an activity of >■• e t watts = — 1 watts. 100,000,000 This activity must be equal to the activity exerted mechan- r ! ically by the system, so that we have the equation, v f __ (B Iv i 10,000,000 ~~ 100,000,000 *. From which, f = dynes. 10 J \ — will be the number of C. G. S. units of current, since the ' 10 C. G. S. unit of current is 10 amperes, so that the funda- mental expression for the electro-dynamic force exerted on a I straight wire, lying or moving at right angles across a uni- j form flux, is / = / = — g— or —^r- grammes weight, 901 9,010 and since 453.6 grammes make one pound,/, expressed in pounds weight will be / = -z- pounds weight. i J 10 x 981 X 453-6 F 6 j" If, for example, the rod shown in Fig. 196 had a length of ; one metre, or 100 centimetres, and moved in the earth's flux whose horizontal component = 0.2 gauss, then if supplied 1 with a uniform current of 1,000 amperes, it would exert a downward force of 0.2 x 100 x — = 2,000 dynes; or ap- 10 proximately, 2 grammes weight. Digitized by VjOOQ IC 246 ELECTRO-DYNAMIC MACHINERY. 297. We have heretofore considered the wire as lying at right angles to the flux through which it is moved. If, how- ever, the wire A B, lies obliquely to the flux, at an angle ft, as is represented in Fig. 197, then the effective length of the wire, or the projected length of AB, at right angles to the flux will be a b. In symbols this will be / sin ft, and the electro- dynamic force will be / = (fc / sin ft — dynes. 298. Although such a machine as is represented in Fig. 196 is capable of performing mechanical work, and might be, therefore, regarded as a form of electro -dynamic motor, yet all FIG. 197. — WIRE LYING OBLIQUE TO MAGNETIC FLUX. practical electro-dynamic motors are operated by means of conducting loops, capable of rotating about an axis. We shall, therefore, now consider such forms of conductor. 299. If the rectangular loop a a" a"' a"", Fig. 198, placed in a horizontal plane, in a uniform magnetic flux, be capable of rotation about the axis 00, then if a current of /amperes be caused to flow through the loop in the direction a' a" a' n a"", electro-dynamic forces will be set up, according to the preced- ing principles, upon the sides a' a" ', and a'" a"", but there will be no electro-dynamic force upon the remaining two sides. Under the influence of these electro-dynamic forces, the side a' a", will tend to move upwards, and the side a'" a"" 9 down- wards. The loop, therefore, if free to move, will rotate, and will occupy the successive positions b, c and d. At the last named position, the plane of the loop being vertical, although the electro-dynamic force will still exist, tending to move the the side a' a", downwards, and the side a'" a"", upwards, yet Digitized by VjOOQ LC ELECTRO-DYNAMIC FORCE. 247 these forces can produce no motion, being in opposite direc- tions and in the same plane as the axis; or, in other words, the loop considered as a rotatable system is at a dead po'nt. 300, It is clear, from what has been already explained, that if the direction of the current in the loop had been reversed while the direction of the field flux remained the same ; or, if the direction of the field flux be reversed with the direction of current remaining the same, that the direction of the electro- dynamic forces would have been changed, tending to move the side a' a", upwards and the side a'" a"'\ downwards, so that the loop would have rotated in the opposite direction until it reached the vertical plane. Consequently, when a loop, lying FIG. I98. — LOOP OF ACTIVE CONDUCTOR IN MAGNETIC FLUX. in the plane of the magnetic flux, receives an electric current it tends to rotate, and, if free, will rotate until it stands at right angles to the magnetic flux. 301. An inspection of the figure will show that when the loop is in the plane of magnetic flux, that is to say, when the rotary electro-dynamic force is a maximum, the loop contains no magnetic flux passing through it, while when the loop is in the vertical position, and the rotary power of the electro- dynamic force is zero, it has the maximum amount of flux passing through it. The effect of the electro-dynamic force, therefore, has been to move the conducting loop out of the position in which no flux passes through it, into the position in which the maximum possible amount of flux passes through it, under the given conditions. m 1! I« *:> Digitized by VjOOQ LC 248 ELECTRO-DYNAMIC MACHINERY, 302. When an active conductor is bent in the form of a loop, such, for example, as is shown in Fig. 199, all the flux pro- duced by the loop will thread or pass through the loop in the same direction, and this direction will depend upon the direc- tion of the current around the loop. If, for example, we con- sider the loop a 1 a* a* a\ independently of the magnetic flux into which it is introduced, and send a current of i amperes, in the same direction as before around the loop, the general dis- tribution of the flux around the sides of the loop is represented FIG. 199. — DIAGRAM SHOWING COINCIDENCE IN DIRECTION OF FLUX PATHS AROUND A LOOP OF ACTIVE CONDUCTOR. by the circular arrows, from which it will be seen that all the flux passes downward through the loop as represented by the large arrow. If this loop be now introduced into the external magnetic flux, as shown in Fig. 192, it will tend to rotate, until the external magnetic flux passes through it in the same direc- tion as the flux produced by its own current. Generally, therefore, it may be stated that when an active conducting loop is brought into a magnetic field, the electro-dynamic force tends to move the loop until its flux coincides in direc- tion with that of the field. 303. During the rotation of the loop as shown in Fig. 198 from the position 0, to the position d, the loop will embrace a certain amount of flux, say $ webers, from the external field. In other words, in the position d 9 the loop holds # webers more flux than in the position a. If the current i amperes, passing through the loop be uniform during the Digitized by VjOOQ LC ELECTRO-DYNAMIC FORCE. 249 rotation, then it can readily be shown that the amount of work performed by the loop during this motion is, W = — • ergs, but this motion comprises only one quarter of a complete revolution. At the same rate the work done in one revolu- tion would be, 4* # 10 ergs = — ' 4 1 # 10 x 10,000,000 joules. 304. In a bipolar motor with a drum-wound armature on which there are w wires, counted once completely around the ' w w periphery, or — loops over the surface, there will be — times as much work performed in one revolution as though a single loop existed on the surface; the work-per-revolution will, therefore, be Aft W . , -joules. 100,000,000*2 If now the motor makes n revolutions per second, the work performed will be n times this number of joules in a second, or 4/ $ *g w watts. =- 2 t $ nw watts. 100,000,000 *2 100,000,000 Then, as will be shown hereafter, the current supplied at the brushes of the motor will be I = 2 i amperes, if 1, be the cur- rent through each loop, so that the activity absorbed by the motor will be, I $ nw - watts. 100,000,000 We know that the E. M. F. of a rotating armature is # n w e =- volts (see par. 132), 100,000,000 so that we have simply, that the activity absorbed by the motor armature available for mechanical work is e I watts, and this must be true under all conditions, in every motor. When an E. M. F. of E volts acts in the same direction as a current / amperes; /. e., drives the current, it does work on the current with an activity of E I watts, the activity being expended by the source of E. M. F. On the other hand, when an E. M. F. of E volts acts in the opposite direction to Digitized by VjOOQ LC [ *5° ELECTRO-DYNAMIC MACHINERY. 5 a current of / amperes, and therefore opposes it, or is a [■ C. E. M. F. to the current, the current does work on the \ C. E. M. F. with an activity of E I watts, and this activity i appears at the source of C. E. M. F. If the C. E. M. F. be I merely apparent in a conductor containing a resistance R ohms, as a drop / R volts, the activity E I = /• R y and is expended in the resistance as heat. If the C. E. M. F. be x caused by electro-magnetic induction, as in a revolving motor armature, the activity E I, is expended in mechanical work, including frictions of every kind. Digitized by VjOOQ IC CHAPTER XXV. MOTOR TORQUE. 305. We now proceed to determine the values of the rotary effort of a loop af different positions around the axis. This rotary effort is called the torque. Torque may be defined as the moment of a force about an axis of rotation. The torque is measured by the product of a force and the radius at which it acts. Thus, if in Fig. 200, a weight of P, pounds, be sus- pended from the pulley Y 9 and, therefore, acts at a radius / feet, the torque exerted by the weight about the axis will be P I pounds-feet If P, be expressed in grammes, and /, in centimetres, the torque will be expressed in gramme-centi- metres; and if P, be in dynes and /, in centimetres, the torque a b c Y © FIG. 200. — DIAGRAM ILLUSTRATING NATURE AND AMOUNT OF TORQUE. will be expressed in dyne-centimetres. Thus, at A y Fig. 2oo > the torque about the axis of the pulley Y, is 400 pounds-feet. At B, it is 800 pounds-feet. At C, it is 400 pounds-feet. As an example of the practical application of torque in electric motors, let us suppose that the pulley P, is attached to the armature shaft of a motor, and that the motor succeeds in raising the weight Jf, by the cord over the periphery of the pulley, then the motor will exert a torque at the pulley of M I pounds-feet Thus, if the pulley be 12 inches in diameter = 0.5 foot in radius, and the weight be 100 pounds, then if the thickness of the cord be neglected, the torque 251 Digitized by VjOOQ LC 252 ELECTRO-DYNAMIC MACHINERY, exerted by the motor will be ioo x 0.5 =50 pounds-feet, about the shaft, at the pulley. 306. The work done by the torque which produces rotation through an angle /?, expressed in radians, is the product of the torque and the angle. Thus, if the torque r, rotates the sys- tem through unit angle about an axis, the torque does an amount of work = r. If the torque be expressed in pounds- feet, this amount of work will be in foot-pounds. If the torque be expressed in gm.-cms., the work will be expressed in cm.- gms., and finally, if the torque be expressed in dyne-cms. the work will be expressed in cm. -dynes, or ergs. Since there are 2 it radians in one complete revolution, the amount of work done by a torque r, in one complete revolution will be 2 n r units of work. For example, the motor in the last paragraph, which produced a torque of 50 pounds-feet, would, in one revolution, do an amount of work represented by 50 x 2 n = 314. 16 foot- pounds. It is evident, in fact, that since the diameter of the pulley is one foot, one complete revolution will lift the weight M 9 through 3.1416 feet, and the work done in raising a 100-pound weight through this distance will be 314.16 foot- pounds. Similarly, if go, expressed in radians per second, be the angular velocity produced by the torque, then the activity of this torque will be r go units of work per second. For example, a motor making 1,200 revolutions per minute, or 20 revolutions per second, has an angular velocity of 20 x 27c = 125.7 radians per second. If the torque of this motor be 10,000 dyne-cms., the activity of this torque; /. e., of the motor, will be 10,000 x 125.7 = 1,257,000 ergs per second 1 = 0.1257 watt. 307. A torque must necessarily be independent of the radius at which it is measured. Thus, if a motor shaft is capable of lifting a pound weight at a radius of one foot; 1. e. y of exerting a torque of one pound-foot, then it will evidently be capable of supporting half a pound at a radius of two feet, or one third of a pound at a radius of three feet, etc. In each case the torque will be the same; /. e. y one pound-foot. 308. The torque produced by a loop, situated in a uniform magnetic flux, varies with the angular position of the loop. Digitized by VjOOQ LC MOTOR TORQUE. *53 For example, returning to Fig. 198, the torque of the active loop is zero in the position d 9 and is a maximum in the position a. The electro-dynamic force exerted by the side a' a" will be (B / — dynes, and, if the radius at which this acts 10 ' about the axis — 1. e., half the length of the side a' a"", be a •cms., then torque exerted by this side will be dynercms. Similarly, the torque exerted in the same direction around the FIG. 201. — DIAGRAM SHOWING SMALL ANGULAR DISPLACEMENT ABOUT ITS AXIS, OP A LOOP IN UNIFORM MAGNETIC FLUX IN ITS PLANE. axis by the side a'" a"\ will be also dyne-cms., so that . 10 the total torque around the axis will be dyne-cms. If the loop moves under the influence of this torque through a Tery small angle dfi, the work done will be r d B = * d 6, 10 l>ut a d /3 = ds y the small arc moved through, as shown in Fig. 201, so that the work done will be . The 10 amount of flux linked with the loop during this small movement will be 2 cos fi, where /?, is the angle included between the plane of the loop and the direction of magnetic flux. The torque exerted bf the loop, therefore, varies as the cosine of the angle between the plane of the loop- and the direction of the external flux. 309. Let us now consider the application of the foregoing- principles to the simplest form of electro-magnetic motor. For this purpose we will consider a smooth-core armature A, Fig. 203, situated in a bipolar field. We will suppose that the total magnetic flux passing through the loop of the wire in the position shown, from the north pole N y to the south pole S 9 is # webers, and that a steady current of i amperes, is maintained through the loop of wire attached to the armature core. In the position of the loop as shown in Fig. 203, there will be no- Digitized by VjOOQ LC MOTOR TORQUE. *55 rotary electro-dynamic force exerted upon the wire, and the armature will be at a dead point. If, however, the armature be moved from this position into that shown in Fig. 204, so that it enters the magnetic flux, assumed to be uniformly dis- tributed over the surface of the poles and armature core, then a rotary electro-dynamic force is set up on the wire, and com- FIG. fl03.— DRUM ARMATURE WITH SINGLE TURN OF ACTIVE CONDUCTORS AT DEAD POINT. municated from the wire to the armature core on which it is / d * secured. The torque being — . -=-27- dyne-cms., where/, is the 10 a p d 9 current strength in amperes, and -7-^ the rate at which flux^n- u p closed by the loop is altered per unit angle of displacement. If, for example, the total flux # = 1 megaweber, and the polar FIG. 204. — ACTIVE CONDUCTOR ENTERING POLAR FLUX. angle over which we assume that this flux is uniformly dis- 2 it tributed is 120 , or = — radians, then the rate of emptying flux from the loop during its passage through the polar arc will 1 000 000 1,500,000 be — = ~ — - — webers-per-radian, and if the strength 2 n n T of current in the loop be maintained at 20 amperes, the torque exerted by the electro-dynamic forces around the armature shaft 20 1,500,000 will be — X — — = 955,000 dyne-cms. Since a torque; Digitized by VjOOQ IC 256 ELECTRO-DYNAMIC MACHINERY. of 1 pound-foot = 13,550,000 dyne-cms., this torque would be gee OOO represented by -^- = 0.0705 pound-foot, or 0.0705 pound at one foot radius. The armature will continue' to move under this torque, if free to do so, until the position of Fig. 205 is reached, where ... ■ ■• T' CZ -^ Tf ■ ■ ■ FIG. 205. — ACTIVE CONDUCTOR LEAVING POLAR FLUX. it is evident that a still further displacement will not increase the amount of flux threaded through the loop. The amount of work which will have been performed by the electro-dynamic forces during this angular displacement of 120* or — radians, will have been r ft = 955,000 X = 2,000,000 3 3 ergs, or, simply — w = — x 1,000,000 = 2,000,000 ergs = 0.2 joule. 310. The armature may continue by its momentum to move past the position of Fig. 205, to that of Fig. 206. As soon as it Nta r fifr r ?£Jg:zz 2 FIG. 206. — ACTIVE CONDUCTOR RE-ENTERING POLAR FLUX, AND ACTED ON BY OPPOSING ELECTRO-DYNAMIC FORCE. reaches the latter position, a counter electro-dynamic force will be exerted upon it, tending to arrest and reverse its motion. Consequently, if the electro-dynamic force is to produce a con- tinuous rotation, it is necessary that the direction of the cur- rent through the coil be reversed at this point; /. e. y commuted, or the direction of the field be reversed as soon as this point is Digitized by VjOOQ LC MOTOR TORQUE. 257 reached. As it is not usually practicable to reverse the field, the direction of current through the coil is reversed by means of a commutator, so that when the position of Fig. 206 is reached, the current is passing through the wire in the opposite direction to that as shown by the arrow. Under these circum- stances, the electro-dynamic force and torque continue in the same direction around the axis of the armature and expend another 0.2 joule upon the armature in its rotation to the original position shown in Fig. 203. It is to be remembered that the representation of the flux in Figs. 203-206 is diagrammatic, since the flux in the entrefer is rarely uniform, never terminates abruptly at the polar* edges, and is, moreover, affected by the flux produced around the active conductor. 311. The total amount of work done in one complete revolu- tion of the armature upon a single turn of active conductor is, 2 i 2 1 ' therefore, ergs, or joules. 10 100,000,000 If the load on the motor be small, so that the momentum of the armature can be depended upon to carry it past the dead- points which occur twice in each complete revolution, the armature will make, say n, revolutions per second, and the amount of work absorbed by the armature loop in this time will be : — joules in a second, or an activity of 100,000,000 J J 2 * * * = watts. 100,000,000 The E. M. F. generated by the rotation of this loop through the magnetic field, by dynamo action, will be 100,000,000 volts, (Par. 132) where w> in this case is 2, since there are two conductors upon the surface of the armature, counting once completely around. The C. E. M. F. will, therefore, be volts, and the activity of the electric current 100,000,000 * J 2 / ti upon this C. E. M. F. will be watts, as above. 100,000,000 Hence it appears that in this, as in every case, the torque and work produced by an electro-magnetic motor depends upon the C. E. M. F. it can exert as a dynamo. Digitized by VjOOQ LC 258 ELECTRO-DYNAMIC MACHINERY. 312. Fig. 207 represents a Gramme-ring armature, carrying a single turn of conductor, situated in a bipolar field. If the total useful flux through the armature is $ webers, as before, half of this amount will pass through the turn, or — webers, 2 since the flux divides itself into two equal portions, as repre- sented in the figure. It will be evident, as before, that start- ing at the position of Fig. 207, there will be no rotary electro- dynamic force exerted upon the loop, until it enters the flux. r """•8 FIG. 207. — GRAMME-RING ARMATURE WITH SINGLE TURN OF ACTIVE CON- DUCTOR AT DEAD POINT. assumed to commence beneath the edge of the pole-piece, and / d& the torque will then be uniform at the value — '7~7t dyne- centimetres, until the turn emerges from beneath the pole-piece 1 $ at Z. The work done in this passage will have been -* • — ergs, and this work will have been taken from the circuit, and, therefore, from the source of E. M. F. driving the current i y and will be liberated as mechanical work (including frictions). If, by the aid of the commutator, the direction of the current around the loop be reversed, the turn, when caused, either by momentum or by direct displacement, to enter the field at £ y Fig. 208, will again receive a rotary electro-dynamic force whose torque is — . — until the angle /?, has been again 10 dp passed, when the work performed will be — — * ergs, as be- fore. The total work done upon the armature in one revolu- i i tion will, therefore, be '2 x — X — = — ergs, and if the 10 2 10 armature make n revolutions per second, the activity expended i n i

55°> 000 If, however, the armature be series-connected, so that there are only two circuits through it, and there are/, poles in the field frame, the torque will be P i $w 2 20 n x 13,550,000 pounds-feet. 315. In a smooth-core armature, the electro-dynamic force, and, therefore, the torque, is exerted upon the active con- ductors, that is to say, the force which rotates the armature acts on the conductors which draw the armature around with Digitized by VjOOQ LC MOTOR TORQUE. 261 them. Consequently, a necessity exists in this type of motor to attach the wires securely to the surface of the core in order to prevent mechanical displacement. 316. In a toothed-core armature, where the wires are so deeply embedded in the surface of the core as to be practically surrounded by iron, the electro-dynamic force or torque is ex- erted on the mass of the iron itself, and not on the wire. That is to say, the armature current magnetizes the core, and the mag- netized core is then acted upon by the field flux. As soon as the iron of the armature core becomes nearly saturated by the flux passing through it, the electro-dynamic force will be exerted in a greater degree upon the embedded conductors, but, under ordinary conditions, the electro -dynamic force which they re- ceive is comparatively small. A toothed-core armature, there- fore, not only serves to protect its conductors from injury, since they are embedded in its mass, but also prevents their receiving severe electro-dynamic stresses. It is not surprising, therefore, that the tendency of modern dynamo construction is almost entirely in the direction of toothed-core armatures. 317. It might be supposed that the preceding rule for cal- culating the value of the torque in a motor, whether running or at rest, would only hold true where there existed a fairly uniform distribution of the field flux, such as would be the case where there was no marked armature reaction. Observations appear to show, however, that if we take into consideration the actual resultant useful flux which enters the armature from any pole, the torque will always be correctly given by the pre- ceding rule, even when the armature reaction is very marked. That is to say if #, be the total useful flux passing through i $ w the armature from one field pole, the torque will be dyne-centimetres, no matter how much flux may be produced independently by the M. M. F. of the armature. 318. We have hitherto studied the fundamental rules for calculating the torque in the case of any continuous-current motor, whether bipolar or multipolar. It . is well to observe that in practice the torque available from a motor at full load Digitized by VjOOQ IC 262 ELECTRO-D YNA MIC MACHINERY. can be determined without reference to either the amount of useful flux passing through the armature, or to the amount of full-load current strength. ' For, if the full-load output of a motor be P watts, and the speed at which it runs be n revolu- tions per second, then the work done per secdnd will be 10,000,000 P ergs. The angular velocity of the shaft will be 2 it n radians, and the torque, will, therefore be, __ 10,000,000 P 2 7t n 10,000,000 P I 3»55°» 000 2 n n dyne-centimetres, pounds-feet. P r = 0.1 1 74 — pounds-feet. For example, if a motor gives six horse-power output at full load, and makes 600 revolutions per minute, required its torque. Here the output, P, = 4,476 watts, the speed in revolutions p per second n = 10, — = 447.6, and the torque exerted by the n motor at full load will be, r = 0.1 174 x 4,476 = 52.55 pounds-feet. If the amount of torque which the motor has to exert in order to start the load connected with it never exceeds the torque when running at full load, then the current which will be re- quired to pass through the armature in order to start it will not exceed the full load current. 319. It is sometimes required to determine what amount of torque must be developed by a motor armature in order to operate a machine under given conditions. For example, if a machine has to be driven with an activity of ten horse-power, at a speed of 300 revolutions per minute, what will be the torque exerted by the motor running at 900 revolutions per minute, suitable countershafting being employed between machine and motor to maintain these speeds ? If we employ the formula in the preceding paragraph, we find for the power P = 10 x 746 = 7,460 watts. The speed n = -~ — = 5 revolutions per Digitized by VjOOQ LC MOTOR TORQUE. 263 second, so that the torque exerted at the shaft of the machine is r = a,.74 £ = o.xx 74 X 7 -f°= ,,5.. pounds-feet. The velocity-ratio of motor to machine is - - = 3, so that the 300 torque exerted by the motor, neglecting friction-torque in the countershafting will be /J * = 58.37 pounds-feet or 58.37 3 pounds at 1 foot radius. Or, we might consider that the motor would, neglecting frictional waste of energy in countershafting, be exerting a QOO power P of 10 x 746 = 7,460 watts at a speed of n = ^— = 15 revolutions per second. Its torque would then be, by the same •P O.H74 X 7,460 n , r . formula, r = 0.1174 — = iiJ— — 58.37 pounds-feet. n 15 320. In some cases it is necessary to determine the torque which must be exerted by a street-car motor at maximum load. It is not sufficient that the motor shall be able to exert a maxi- mum activity of say 20 H. P. It is necessary that it shall be able to exert the given maximum torque at a definite maximum speed of rotation, and, therefore, the given maximum activity of 20 H. P. Otherwise, the motor might be of 40 H. P. capacity, and, yet by failing to exert the required torque, might be unable to start the car, or, in other words, the motor would have too high a speed. For example, required the torque to be exerted by each of two single-reduction motors in order to start a car with 30" wheels weighing 6 short tons light, and loaded with 100 passengers, up a ten per cent, grade, the gearing ratio of armature to car wheel being 3 to 1. Here 100 passengers may be taken as weighing 15,000 lbs. or yj4 short tons. The total weight of the car is therefore 27,000 lbs. The frictional pull required to start a car from rest on level rails, under average commercial conditions, is about 1.8 per cent, of the weight, or, in this case, 486 lbs. weight. The pull exerted against gravity is also 2,700 lbs., making the total pull 3,186 lbs. weight. The 30 radius of the car wheel being — = 1.25 feet, the torque at the car 24 Digitized by VjOOQ IC 264 ELECTRO-DYN+MIC MACHINERY. wheel axle is 3,186 x 125 = 3,983 pounds-feet. The torque at the motor shafts is therefore 3 ' 9 = 1,328 pounds-feet, and o each motor must therefore exert — — = 664 pounds-feet. 2 If the motors make 600 revolutions per minute or 10 revolu- tions per second, exerting this torque, their activity will be 664 x 10 x 2 n x 1. 355 = 5 6 ,53° watts, = 56.53 KW, and their combined activity 113.1 KW, neglecting gear frictions. 321. Considering the case of a motor armature in rotation, the speed of its rotation for a given E. M. F. applied to its armature terminals will depend upon three things : viz., (1.) The load imposed upon the armature, or the torque it has to exert. (2.) The electric resistance of the armature in ohms. (3.) Its dynamo-power ; i. e., its power of producing C. E. M. F., or the number of volts it will produce per revolution per second. If E y be the E. M. F. in volts applied to the armature termi- nals, r, the torque, which the motor has to exert, including the torque of frictions, in megadyne-decimetres (dyne-cms. X io~ 7 ) r, the resistance of the motor armature in ohms, and e y the C. E. M. F. produced in volts per revolution per second of the ip ^__ „ ^ armature. Then n e, will be the total C. E. M. F. . will r be the current strength received by the armature according to Ohm's' law. The activity of this current expended upon the C. E. M. F. will be their product, or n e x — — — watts, and this must be equal to the total rate of working, or 2 n n r, = consequently, ne ( J = 2 n n r and n = 2 n — r revolutions per second. For example, if a motor armature, whose resistance is 2 ohms, has a uniformly excited field, which may be either of the bipolar or multipolar type, and is supplied with 500 volts at its terminals ; and if the C. E. M. F. it produces by revolution in the field is 40 volts per-revolution-per-second, then the speed Digitized by GOOglC MOTOR TORQUE. 265 at which the motor will rotate, when exerting a torque, including all frictions, of 100 pounds-feet (100 x 13,550,000 dyne-centi- metres, = 135.5 megadyne-decimetres) will be 500 27t X 2X 135-5 * , *. n = 2 ^-^ = 12-5 — 1.06 == 11.44 revolutions- 40 1,600 J ^ per-second. 322. It will be observed from the above formula that if either the torque be zero, or the resistance of the armature is p zero, the speed of the motor will simply be — revolutions-per- second. Or, in other words, that the armature will run at such a speed that its C. E. M. F. shall just equal the E. M. F. applied to the armature ; 1. e. without drop of pressure in the armature. If the torque could be made zero, the motor would do no work and would require no current to be supplied to it, so that no matter what the resistance of the armature might be, the drop in the armature would be zero. All motors necessarily have to exert some torque in order to over- come various frictions, but on light load their speed approxi- mates to the value — revolutions-per-second. If the resistance of the motor is very small, which is approximately true in 2 7t T T the case of a large motor, the second term — ^ — , in the formula, becomes small, and the diminution in speed due to load is, therefore, also small. In other words, the drop which takes place in the armature due to its resistance is correspond- ingly reduced, permitting the motor to maintain its speed and C. E. M. F. of rotation. Fig. 209 represents diagrammati- cally a motor armature revolving in a suitably excited magnetic field, and supplied from a pair of mains, M, M, with a steady pressure of 500 volts. The resistance of the arma- ture is represented as being collected in the coil r, while the C. E. M. F. of the motor is indicated as opposing the passage of the current from the mains. The drop in the resistance is represented as being 40 volts, while the C. E. M. F. is 500 — 40, or 460 volts. 323. The E. M. F. applied to the terminals of a motor armature, therefore, has to be met by an equal and opposite or Digitized by VjOOQ IC 266 ELECTRO-DYNAMIC MACHINERY. C. E. M. F. in the armature, which is composed of two parts, that due to rotation in the magnetic flux, or to dynamo- electric action, and that apparent C. E. M. F. which is entirely due to drop of pressure in the resistance of the arma- ture, considered as an equivalent length of wire. The activity expended against the C. E. M. F. of rotation is activity expended in producing torque, and, therefore, almost all available for producing useful work, while the activity expended against the C. E. M. F. of drop is entirely expended in heating the wire. As the load on the motor is increased, the current FIG. 209. — DIAGRAM REPRESENTING RESISTANCE AND C E. M. F. IN A REVOLVING MOTOR-ARMATURE. which must be supplied to the motor to overcome the addi- tional load or torque increases the drop in the armature, and, therefore, diminishes the C. E. M. F. which has to be made up by rotation, and the speed falls, or tends to fall, in proportion. 324. When a motor armature is at rest, its C. E. M. F. of rotation is zero, and the C. E. M. F. which it can produce under these conditions must be entirely composed of drop of pressure. In other words, the current which will pass through it is limited entirely by the ohmic resistance of the circuit. If /, be the current strength in amperes supplied to a motor armature at a pressure of E volts, the activity expended in the armature will be E i watts. The activity expended in produc- Digitized by VjOOQ IC MOTOR TORQUE. 267 ing torque will be n e i watts, so that disregarding mechanical and electro-magnetic frictions, the efficiency of the motor will be -=r^ = -ft, or simply the ratio of the C. E. M. F. of rota- tion to the impressed £. M. F. This is a maximum at no load ; /. e. y when the motor does no work, and is zero when the motor is at rest. The value oi t, the volts-per-revolution-per-second, is in all cases of multiple-connected armatures equal to $ w x i°~ 8 > where &, is the number of webers of flux passing usefully into the armature from any one pole, and w 9 is the number of turns of conductor counted once around its periphery. 325. The speed of a motor, therefore, varies, to the first ap- proximation, inversely as the useful magnetic flux, and in- versely as the number of armature conductors. A slow-speed motor, other things being equal, is a motor of large flux, or large number of turns, or both, and, as will afterward be shown, in order to decrease the 6peed at which the motor is running, it is only necessary to increase, by any suitable means, the use- ful flux passing through its armature. « 326. Just as in the case of a generator armature, whose maximum output is obtained when the drop in its armature is equal to half its terminal E. M. F. (Par. 9), so in the case of the motor, the? output is a maximum (neglecting frictions), when the drop in the armature is half the E. M. F. applied at the armature terminals, or, in symbols, when «yMER StAlJ FFIOjj NOV_ / ^- > O I 80 u. u. u 9fc / / w 7» < S70 Id ae £66 60 66 60 S 55 6 7 •6 1( X) is 86 1 So r » soq KILOWATT8 OUTPUT FIG. 2IO. — COMMERCIAL EFFICIENCY CURVE OF MOTORS AT FULL LOAD. from motors of varying capacity up to 200 KW. This curve has been plotted from a number of actual observations with machines constructed in the United States. 334. It is to be remembered, however, that the full load efficiency of a motor is not always the criterion upon which its suitability for economically performing a given service is to be determined. It not infrequently happens that the character of the work which a motor has to perform is necessarily exceed- ingly Variable, so that the average load might not be half the full load of the machine. Under such conditions, the average efficiency is of more importance than the ftdl-loa£ efficiency. Were the efficiency curve of all motors in relation Digitized by VjOOQ LC EFFICIENCY OF MOTORS. 271 to their load of the same general outline, the average efficiency would be, approximately, the same in all motors having the same full-load efficiency. As a matter of fact, however, the efficiency curves of different machines may be very different. Thus one machine may have its maximum efficiency at half load, and behave at full load, in regard to its efficiency, as though it were actually overloaded, while another machine, with the same full-load efficiency, may show a lower efficiency at half load. Obviously the first machine would be preferred for variable work, other things being equal. 335. Similar considerations apply to electric generators. The full-load efficiency is not in every case the ultimate criterion of economical delivery of work, but it generally happens that generators are installed in such a manner, and under such conditions, that a nearer approach to their full load is attained, so that ordinarily the shape of the efficiency curve of a generator is not of such great importance as that of a motor. Fig. 211 represents the efficiency curves of two motors, each having a full-load efficiency of 78 per cent One of these machines has an efficiency, at about two-thirds load, of 84 per cent, but at overloads is inefficient, while the other becomes more efficient at slight overloads. 336. In order to produce a motor of given full-load efficiency with comparatively small loss at moderate loads, and, there- fore, a comparatively heavy loss at heavy loads, we may em- ploy a slow-speed motor y or a motor which shall generate the necessary C. E. M. F. at a comparatively low speed. Such a machine will probably. have a small loss in mechanical friction, because of its lower speed of revolution. It will, similarly, have, probably, a small loss in hysteresis and eddy currents for the same reason, but a slow speed motor will probably have a greater number of armature turns in order to com- pensate for the smaller rate of revolution, and the I*R loss in the armature is, therefore, likely to be greater at full load. In such a machine, the loss at full load is principally due to PR; and, since this loss decreases rapidly with /, it will evidently have a small loss at moderate loads. Digitized by VjOOQ IC *7 2 ELECTRO-DYNAMIC MACHINERY. 337; The speed at which a motor will run in performing a given amount of work varies considerably with different types of motors. For example, of two motors of 20 KW capacity, one may run at 400 revolutions-per-minute, and the other at 1,000 revolutions-per-minute. It is evident that the first machine will have two and a half times the full-load torque of the second. The lower speed is, however, generally speaking, only to be obtained at the expense of additional copper and iron ; that is to say, the cost of material in a slow-speed machine will, probably, be greater than the cost of material 100 5* Z M *^ H Ik Ik M i t0 i III 2 z III "* 80 y i PR( y 5FORT ON OF 9 LOAD 1 J j 3 li > FIG. 211. — EFFICIENCY CURVES OF TWO DIFFERENT MOTORS HAVING SAME FULL-LOAD EFFICIENCY. in a high-speed machine of the same output and relative excel- lence of design. It becomes, therefore, a que&tion as to the relative commercial advantage of slow speed versus high speed in a motor. 338. Motors are generally installed to drive machinery either by belts or" gears, and the belt speed or the gear speed of machinery is, in practice, a comparatively fixed quantity. If, Digitized by VjOOQ IC EFFICIENCY OF MOTORS. *73 therefore, the speed of the motor be greater than the speed of the main driving wheel of the machines with which the motor is connected, intermediate reducing gear or countershafting has to be installed. This adds to the expense of installation, not only in first cost, but also in maintenance, lubrication, and the continuous loss of power it introduces through friction. The result is, that up to a certain point, slow-speed motors are •economically preferable, and the tendency of recent years has been toward the production of slower speed dynamo machinery. In comparing, therefore, the prices of two motors of equal output, the speed at which they run has to be taken into account, as well as the efficiency at which they will operate. It is to be remembered that any means in the design which will enable a motor to supply its output at a slower speed, are equivalent to means which will enable a motor of the higher speed to supply a greater output. 339. The weight of .a motor is a matter of considerable im- portance in cases of locomotors ; i. e., of travelling motors, as in the case of electric locomotives, street-car motors or launch motors, but in the case of stationary motors, their weight is of less consequence, since, after freight has been once paid for their shipment, no extra expense is entailed by reason of their increased mass when in operation. Indeed, weight is often a desirable quality for a motor to possess in order to ensure steadiness of driving, although undue weight in the armature is apt to produce frictional loss, and diminished efficiency. 340. In comparing the relative weights of motors, two cri- teria may be established; namely, (1) In regard to torque, and (2) in regard to activity. In some cases, the work required from the motor is such that the pull or torque which must be given in reference to its weight is the main consideration, while in other cases it is not the torque, but the output per-pound of weight, which must be considered. 341. The torque-per-pound, in the case of street-car motors, where lightness is an important factor, has been increased to Digitized by VjOOQ IC 274 ELECTRON YNAMIC MACHINERY. 133,000 centimetre-dynes per-ampere, per-kilogramme of weight; or, 0.0045 pound-foot per-ampere per-pound of total motor weight, exclusive of gears, so that a 500-volt street-car motor, weighing 223 pounds, and supplied with one ampere of current, would exert a torque of one pound-foot. In stationary motors, the torque is usually only 0.001 to 0.0015 pound-foot per-ampere per-pound of .weight, or about four times less than with street-car motors. This is owing to the fact that cast iron is more largely employed in stationary motors, owing to its lesser cost. The output per-pound of weight in motors varies from 5 watts per pound to 15 watts per pound, according to the size and speed of the motor. 342. We may now allude to the theoretical conditions which must be complied with in order to obtain the maximum amount of torque in a motor for a given mass of material. It must be carefully remembered, however, that these theoretical conditions require both modification and amplification, when applied to practice, so that the practical problem is the theo- retical problem combined with the problem of mechanical construction. i $ w 343. The torque of a motor armature being cm.- dynes, we require to make this expression a maximum for a given mass of copper wire in the armature and in the field magnets, neglecting at present all considerations of structural strength. The torque-per-ampere will be cm. -dynes. In order to make this a maximum, both $ and w, should be as great as possible. 344. It is evident that if we simply desired a motor of power- ful torque-per-ampere, regardless of its weight, we should employ as much useful iron as possible, so as to obtain as great a useful magnetic flux $, through the armature, as possible, and we should employ as many turns of wire upon the surface of the armature as could be obtained without mak- Digitized by VjOOQ IC EFFICIENCY OF MOTORS. 275 ing the armature reaction excessive, or without introducing too high a resistance, and too much expenditure of energy in the armature winding. Such a motor would essentially be a heavy motor, so that the requirements of a motor with power- ful torque- per-ampere would simply be met by a motor of great useful weight, and this, indeed, would be obvious without any arithmetical reasoning. 345. When, however, the torque-per-ampere per-pound-of- weight has to be a maximum, the best means of attacking the problem is to consider a given total weight of copper and iron in the armature, and examine by what means this total weight can be most effectually employed for producing dynamo-power; /. e., volts-per-revolution-per-second, and torque-per-ampere. 346. It will, in the first place, be obvious that a long mag- netic circuit will not be consistent with these requirements, since, as we shorten the magnetic circuit, retaining the same mass of material, we make it wider, or of greater section, and so increase the total flux $. In the second place, the material of which the magnetic circuit is formed should have as small a reluctivity, and as powerful a flux density as possible, since this will increase the total flux without adding to the weight. For this reason soft cast steel is much to be preferred to cast iron. 347. Again, it will be evident that as we increase the number of turns on the armature, having determined upon a certain total mass of armature copper, or armature winding space, we increase, according to the formula, the torque-per-ampere. But, in occupying the given winding space with many turns instead of with few turns, we increase, for a given speed, the voltage of the armature. Thus, if a motor armature be intended to rotate at a speed of 10 revolutions per second, its E. M. F., other things being equal, will be 10 times as great, when we use 10 times as many wires upon its surface, and its torque- per-ampere will be also increased 10 times. A high E. M. F. motor is, therefore, necessarily a motor of high torque-per- ampere. A 500-volt armature would, therefore, in accordance with preceding principles, necessarily be a motor of greater Digitized by VjOOQ LC 276 ELECTRO-DYNAMIC MACHINERY. torque-per-ampere than the same armature wound for 10b volts, although the torque at full load might be the same in each case, since the low-pressure armature might make up by in- crease of current what it lacked in torque-per-ampere. 348. Having selected a field frame with as short a magnetic circuit as is consistent with not excessive magnetic leakage, and with room for magnetizing coils, and having placed a large number of turns upon the armature surface, there remain several important detail considerations which should be taken into account to enable a high torque-per-ampere to be obtained. 349. In the first place,, the reluctance in the magnetic circuit should be as small as possible in order to diminish the M. M. F. and the mass of magnetizing copper. With smooth-core armatures this would represent a small entrefer and a small winding space, whereas, to obtain many turns, we require a large entrefer and large winding space, so that with a smooth- core armature, a compromise is necessary at some point of maximum effect, depending upon a great variety of details. With toothed-core armatures, however, a large number of turns may be disposed upon the armature surface, yet the reluctance in the entrefer may be comparatively small. This consideration affords an additional argument in favor of toothed-core armatures for high torque. 350. In the second place, the number of poles in the field frame should be as great as possible. If we double the number of poles in the field frame, retaining the same armature, and make suitable changes in the connection of the armature turns, we double the E. M. F. of the armature (Par. 148). Thus, if we have an armature with a given number of turns on its surface and a given speed of rotation, in a bipolar field, and the E. M. F. obtained from the armature is 100 volts, then, if we change the field to a quadripolar frame, and suitably change the con- nection of the armature turns, the E. M. F. of the armature will be 200 volts. If, instead of changing the armature con- nections, we simply change the number of brushes from two to four, and suitably connect these brushes, we obtain only 100 Digitized by VjOOQ IC EFF1CILXCY OF MOTORS. 277 volts as before, but as there are now four complete electric circuits through the armature, we have doubled the load which the armature can sustain without overheating, and, therefore, practically doubled the output of the armature, so that when we double the number of poles covering the armature, assuming the useful flux through each pole to be the same as before, we either double the torque-per-ampere directly, if the armature be series-connected, or we retain the torque-per-ampere with FIG. 212. — QUADRIPOLAR CAR MOTOR WITH TWO FIELD COILS. a multiple-connected armature and, by changing the winding, obtain a greater output from the motor. 351. There will, of course, be a limit to the number of poles which can be employed with any armature without increasing its diameter, since there will only be sufficient room for a cer- tain number of poles carrying a given maximum flux, and also, since the difficulty of magnetizing a greater number of poles will be insuperable, either for want of space, or owing to increased magnetic leakage. The principle, however, is important. 352. The number of turns which can be utilized upon the surface of an armature is itself limited; first, by the resistance Digitized by VjOOQ IC 278 ELECTRO-DYNAMIC MACHINERY. of the armature and consequent excessive heating under load; second, by excessive armature reaction and consequent spark- ing ; and, third, in rarer cases, by the E. M. F. of the circuit, FIG. 213. — QUADRIPOLAR CAR MOTOR WITH FOUR FIELD COILS. and, consequently, the unduly slow speed at which a powerful armature will run on such circuit. 353. The best embodiment of the foregoing principles in ex- isting practice is found in a modern street-car motor. Here a powerful torque-per-ampere, with minimum weight, is desired in order to start a loaded car from rest up a steep gradient. Two forms of such motors are shown in Figs. 212 and 213. 354. Fig. 212 shows a cast-steel quadripolar field frame with two magnetizing coils M, M. These produce not only poles at the opposite sides of the armature, in the cores over which Digitized by VjOOQ IC EFFICIENCY OF MOTORS. 279 they are wound, but also poles at the cylindrical projections P, P> which lie above and below the armature so that there are four complete magnetic circuits through the field frame and armature, two circuits through each magnetizing coil. The brushes B % B y are set 90 degrees apart on the commutator C. The armature A, is of the toothed-core type. 355. In Fig. 213 the same results are obtained with various detailed differences in mechanical construction. There are four poles around the armature, two of which, P 9 P, are seen in the raised cover, and two others are similarly contained in the lower half of the frame. Each of these poles is, in this case, surrounded by a magnetizing coil, M. £, £, are the brushes, set 90 apart from the commutator. The armature, A, is of the toothed-core type. In both of these cases the magnetic circuits are as short as is practically possible, and the useful magnetic flux is as great as possible. Digitized by VjOOQ IC CHAPTER XXVII. REGULATION OF MOTORS. 356. The requirements of a motor depend upon the nature and use of the apparatus which the motor is designed to drive. All these requirements, in relation to driving machinery, may be embraced under three heads; viz., (1.) Control of starting and stopping. (2.) Control of speed, both as to constancy and as to vari- ability. (3.) Control of torque, both as to constancy and as to variability. The above requirements are by no means met to an equal degree by the electric motor. For example, the requirement of constant speed is much more readily dealt with than the requirement of variable speed. 357. The conditions under which motors have to operate may be divided into four classes; namely, (1.) Constant torque and constant speed. (2.) Variable torque and constant speed. (3.) Constant torque and variable speed. (4. ) Variable torque and variable speed. 358. The first two conditions are readily secured, the third and fourth are only secured with difficulty. For example, a rotary pump belongs to the first class. Here the load is con- stant and the speed is presumably constant. The second class comprises the greater number of machine tools, where the speed is constant but the activity is variable. The third class embraces most elevators and hoisting ma- chines. The fourth class is well represented by street-car motors. 359. Any continuous-current electric motor will supply a constant torque at a constant speed when operated at a constant Digitized by VjOOQ LC REGULATION OF MOTORS. 281 pressure. Thus, whether the motor be self-excited or sep- arately-excited, and whether it be shunt-wound, series-wound or compound-wound, it will, if supplied with a constant pres- sure a*t its terminals, and assuming constant frictions in the machine, deliver a constant torque at a constant speed, and taking from the mains supplying it, a constant current strength, and, therefore, constant activity. The condition of constant torque and constant speed is one which is, therefore, readily dealt with by electric motors. The above statement, however, is true only of single motors ; for, if two motors, of any continuous-current type, be con- FIG. 214.— TWO SERIES-WOUND MOTORS COUPLED IN SERIES BETWEEN CONSTANT-POTENTIAL MAINS. nected in series across a pair of constant-potential mains, they will be in unstable equilibrium as to speed under a given load. If the torque on each of the two machines in Fig. 214 were maintained absolutely equal; then, by symmetry, the two series motors represented would run at equal speeds, and absorb equal activities. But should the load on one accidentally increase, even to a small extent, above that of the other, the tendency would be to slow down the over-loaded motor and accelerate the other, so that it would be possible to have one motor at rest exerting a constant torque, and the other motor exerting the same torque at double its former speed. If, how- ever, the two motors are rigidly coupled together to a coun- tershaft, so that their speeds must be alike, then they will behave as a single motor. Consequently, a continuous-current motor employed for pumping or driving a fan, and which, there- Digitized by VjOOQ IC 282 ELECTRO-DYNAMIC MACHINERY. fore, has a constant torque to supply, will run at constant speed when supplied with constant pressure, whatever the type of motor may be. 3(£o. The important requirement of constant speed under variable load is nearly met by a shunt-wound motor. It may be almost perfectly met by the compound-wound motor. It is not met, without the aid of special mechanism, by the series-wound motor. 361. Considering first the case of a shunt-wound motor, represented in Fig. 165, the speed at which the armature will run is — revolutions-per-second (Par. 321), when at no load, pro- vided that the friction of the machine is so small that we may safely neglect the drop of pressure in the armature running light. When the full-load current / amperes, passes through the armature, the speed will be reduced to revolutions-per- second, r, being the armature resistance in ohms. Thus a particular shunt-wound, no-volt motor has an arma- ture resistance (hot) of 0.075 ohm, and its full-load output is 9 H. P. What will be its fall in speed between no load and full load, its no-load speed being 1,395 revolutions-per-minute or 23. 25 revolutions-per-second ? Here, neglecting the armature torque and drop in pressure at no load, e 9 the dynamo power, or volts-per-revolution-per- second = = 4.73. Its output at full load being 9 x 746 2 3- 2 5 = 6,714 watts, and its armature efficiency, say, 0.84, the arma- ture intake will be R = 7,994 watts = 72.68 amperesx no volts. The full-load armature drop will, therefore, be 72.68 x no — 5.45 0.075 = 5-45 volts, and the full-load speed — - = 22.1 4-73 revolutions-per-second, approximately, or 1,326 revolutions- per-minute. The drop in speed of this motor between no load and full load is, therefore, 69 revolutions-per-minute ; or, approximately 5 per cent. Digitized by VjOOQ LC REGULATION OF MOTORS. 283 362. If the variation of speed due to the drop in the armature with the full-load current is greater than that which the con- ditions of driving will permit, then means may be adopted to reduce the value of e, at full load in the above formula, so as to increase the speed in compensation for the necessary drop. This is frequently accomplished by inserting resistance in the circuit of the field magnet so as to reduce its M. M. F., and, consequently, the useful flux which it sends through the armature. A rheostat in the shunt-field circuit, therefore, enables such regulation to be made by hand, as will maintain the speed of a shunt motor constant under all torques within its full load. For most commercial purposes the automatic regulation of the shunt motor is sufficiently close, the rheo- stat only being employed on special occasions. The larger the shunt motor the less the drop in speed which is brought about by the full-load current. Thus a i-H. P. shunt motor will usually drop only 10 per cent, in speed at full load, a 10- H. P. motor 5 per cent., and a 100-H. P. motor, 3 per cent. 363. When a series motor is operated on a series circuit, as for example, on a series-arc circuit, some device is necessary which will regulate the speed of the motor. If no such device were provided, if the starting torque of the motor due to the constant current passing through it, exceeded the torque due to load and frictions combined, the motor would accelerate indefinitely in its endeavor to oppose by C. E. M. F. the passage of the current. If the load were of such a nature that the torque increased with the speed, as in the case of a fan, the speed might be automatically controlled, but, since, in driving machinery, the torque is nearly independent of the speed, a controlling mechanism becomes essential. One method by which this is accomplished is by rotating the rocker arm and brushes into such a position about the com-, mutator, that the useful flux from the constantly excited series- wound field coils, passing through the armature coils, is virtu- ally reduced by passing both into and out of the armature coils when the diameter of commutation is shifted, thereby neutralizing the electro-dynamic force on the windings. The method corresponds to that adopted for varying the E. M. F. of arc dynamos, in order to keep the current Digitized by VjOOQ IC 284 ELECTRO-DYNAMIC MACHINERY. strength constant in the circuit, despite variations of load. (Par. 261.) Fig. 215, represents a. small series- wound -J-H. P. motor for use on series-arc circuits and provided with a hand regulator to control the speed. The rocker arm, which supports the brush-holders, has a projection P f to which an insulating FIG. 21 5. —ONE-SIXTH H. P. MOTOR FOR ARC CIRCUITS WITH HAND OR TREADLE REGULATOR, ROTATING BRUSHES, AND AUTOMATIC CUT-OUT. handle or treadle is attached. Under ordinary conditions, the spiral spring S y pulls the rocker arm^into the position shown, so that the brushes b, b, rest upon the commutator at a diameter at right angles to the diameter of neutral commu- tation in an ordinary bipolar motor, so that the torque of the motor will be reduced to zero. By rotating the rocker arm with handle or treadle against the tension of the spring S, so that the projection P, occupies the position P\ the brushes are brought forward to the position b\ of maximum torque, so that the speed of the motor may be controlled. In the motor represented in Fig. 216, this rotation of the rocker arm is effected automatically by the aid of a. centrifugal governor G, mounted at one end of the armature shaft. Digitized by VjOOQ IC REGULATION OF MOTORS. 285 When the motor is started, by throwing it into the series cir- cuit by a switch, the brushes are at the diameter of neutral -commutation or maximum torque. If the load torque is not too great for the armature to overcome, the motor will accelerate until the governor G, has lifted its wings tcr such a distance by centrifugal force against the tension of its B FIG. 2l6.— ONE-H. P. ARC MOTOR WITH AUTOMATIC GOVERNOR. •spring, that the lever Z, following the motion of the governor, has pulled round the rocker arm and brushes to a diameter at which the torque of the armature is equal to that of the load. 364. In the ordinary motor the speed increases until the current strength I amperes passing the armature at the ter- minal pressure £ volts, limits the intake, E I watts, to the load activity and energy losses combined. In this motor the speed increases until the governor moves the brushes into such a position that the C. E. M. F., E volts, limits the. activity of the constant current I amperes to the amount E I watts, equal to the load activity and energy losses. The speed will, therefore, ^vary with the load by a small amount depending upon the sensibility of the governor. Motors for series-arc circuits are not usually employed above 3 H. P. Owing to the high pressure which may exist Digitized by VjOOQ LC 286 ELECTRO-DYNAMIC MACHINERY. upon their circuits, they may be dangerous to handle unless precautions are taken. 365. When a series-wound motor is employed across con- stant-potential mains, in the manner indicated in Fig. 164, the value of w 9 varies with the torque or load, since any change in the current strength through the armature changes the M. M. F. of the field magnets, and, therefore, the flux d>. The tendency of a series motor is, therefore, to reduce its speed, as the torque imposed upon the motor is increased, and such a motor would run, theoretically, at an infinite speed on light load, if there were no frictions in the armature to be Overcome. A shunt-wound motor, therefore, tends to drop in speed with load to an extent proportional to the drop of pressure in the armature. A series-wound motor falls off in speed with load, not only owing to the drop of pressure in the armature, but also owing to the increase in M. M. F. and flux. 366. A compound-wound motor will, however, maintain its speed practically constant under all loads, if the series winding on the field coils be so adjusted that the increase in current strength through these coils and the armature shall diminish the M. M. F. of the field magnets to the degree necessary to compensate for the drop of pressure in the armature winding. The connections of such a compound-wound motor are the same as for the compound-wound dynamo shown in Fig. 166. 367. Although a series-wound motor is unfitted for maintain- ing a constant speed on constant-potential mains with variable torque, yet it is possible to connect two series-wound machines of the same type and character together, one acting as a gener- ator and the other as a motor, and to obtain a nearly constant speed of the motor by compensatory changes in the E. M. F. of the generator automatically brought about by the variations of load. This case, however, can only apply to a single motor driven by a single generator, and is, therefore, inapplicable to a system of motors driven by a single generating source. Digitized by VjOOQ LC REGULATION OF MOTORS. 287 368. Figs. 217 and 218 are diagrams taken from actual tests of two small 500-volt, #-H. P. motors, of good construction and well-known manufacture, one being a series-wound motor and 200 800 400 WATTS INTAKE FIG. 217. — TEST DIAGRAM OF A^SHUNT-WOUND ONE-HALF H. P. MOTOR SHOWING DISTRIBUTION OF ACTIVITY. the other a shunt-wound motor. The armatures of the two machines and also their field frames were practically identical, the only essential difference between the two being in the field Digitized by VjOOQ IC *88 ELECTRO-DYNAMIC MACHINERY. winding. The weight of the machines was 105 lbs. each, that of the armature nearly 22 lbs. The resistance of the armatures was 40 ohms each, and the resistance of the fields 3,680 ohms for the shunt-wound, and 37.5 ohms for the series-wound, machine. In these diagrams, the ordinates represent the expenditure of activity in the field windings, armature windings, frictions (including hysteresis, eddy currents, and mechanical frictions), and output at the shaft. The abscissas represent the intake in watts. Thus, referring to Fig. 217 for the shunt-wound machine, it will be seen that when delivering full load, or 373 watts, the machine absorbed 690 watts, expending 90 in the field magnets, as P R y 67 watts in the armature as P R, and 160 watts in total frictions. The commercial efficiency of the machine at full load, was, therefore, f^ or 54 per cent. The 690 speed of the machine falls from 29.2 to 25 revolutions-per- second, or from 1,752 to 1,500 revolutions per minute, a drop of 14.4 per cent., and this drop is closely proportional to the output. The highest commercial efficiency reached was 55 per cent, at 340 watts output. Taking now the series-wound machine referred to in Fig. 218, it will be observed that the field loss is much smaller, particu- larly at light loads, owing to the fact that it increases with the current strength, and practically disappears when the current strength is very small. Owing to this fact it will be observed that the commercial efficiency of this machine is greater throughout than that of the shunt machine. At a delivery of 340 watts, the intake was 600 watts, expended as follows : 57 watts in the magnets, 63 in the armature, and 140 watts in frictions. It will be seen, however, that the speed falls from 38.5 to 21.5 revolutions-per-second, or from 2,310 to 1,290 revolutions-per-minute, a drop of 44.2 per cent. It is clear, therefore, that a series- wound machine is, in small" sizes, cheaper to construct than a shunt-wound nfachine, since it employs only a few turns of coarse wire instead of many turns of fine wire in its field coils. It also has a slightly higher efficiency. It also dispenses with the use of a starting rheostat in the arma- ture, but has the disadvantage of possessing a much greater variation in speed under variations of load. Digitized by VjOOQ LC REGULATION OF MOTORS. 289 369. As already mentioned, the condition of constant torque and variable speed is one which it is much more difficult for the electric motor to meet. If it were possible to vary the j»0 800 400 WATT8 IMTJKfl FIG. 218. — TEST DIAGRAM OF A SERIES-WOUND ONE-HALF H. P. MOTOR SHOWING DISTRIBUTION OF ACTIVITY. useful magnetic flux through, the armature within wide limits, the method of varying the M. M. F. of the field magnets would effect the result desired. While, however, it is possible to produce a variation of speed in the ratio of 3 to i, Digitized by VjOOQ IC 290 ELECTRO-DYNAMIC MACHINERY. by varying the M. M. F. ; that is to say, while motors have been constructed, under special conditions, which will run, say at from a maximum of 900, to a minimum of 300 revolutions- per-minute, merely owing to variation in the M. M. F. of their fields, yet such a range is only obtained with great difficulty, owing to the fact that magnetic saturation is reached at maximum M. M. Fs. in the iron constituting the magnetic circuit, and that when the field flux is greatly reduced, the armature reaction at full load is liable to be excessive, with heavy sparking at the commutator. The maximum range of A b c FIG. 219.— DIAGRAM SHOWING ONE METHOD OF SERIES-PARALLEL FIELD EXCITATION IN A STREET-CAR MOTOR. speed in an ordinary shunt motor, brought about by field regulation, is only about 25 per cent, so that a motor whose maximum safe speed is 1,000 revolutions-per-minute, can be reduced to minimum of about 750 revolutions. 370. The M. M. F. of a motor field may be varied electric- ally in two ways; namely, by altering the current strength through the field coils as a whole, by inserting a varied resist- ance in their circuit; and second, by altering the action of certain portions of the field coils relatively to other portions, as, for example, by changing them from series to parallel, or the reverse. In shunt-wound motors, the regulation is ■usually effected by the introduction of a field rheostat. In series-wound motors it is usually effected by varying the number or arrangement of the fi^eld coils. Thus the arrange- ment for connecting the field coils of a particular form of street-car motor is represented in Fig. 219/ It will be seen that there are three coils on each limb of the field, but each Digitized by VjOOQ LC REGULATION OF MOTORS. 291 pair is permanently connected as shown, so that electrically there are only three coils, A, B and C. By the action of the controlling switch, these coils may be connected as shown in the diagram. In Position 1, all three coils are in series, making the rela- tive M. M. F. 3 and the relative resistance 3. In Position 2, one coil is short circuited, making the rela- tive M. M. F. 2 and the relative resistance 2. In Position 3, two coils are connected in parallel, making the relative M. M. F. 2 and the relative resistance 1.5. In Position 4, two coils only are connected in parallel, mak- ing the relative M. M. F. 1 and the relative resistance 0.5. In Position 5, all three coils are connected in parallel, mak- ing'the relative M. M. F. 1 and the resistance 0.333. Fig. 220 represents the characteristic curve of a particular motor of this character, with the flux in megawebers, passing fig. 220.- . AMPERE TOfcNB -CURVE OF MAGNETIC FLUX THROUGH ARMATURE IN RELATION TO M. M. F. OF FIELD MAGNETS. through the armature with different excitations of the field magnets, expressed in ampere-turns. With the aid of this curve it is possible to estimate the range of speed which can be obtained by connecting the coils in different arrangements. For example, at half load of 7^ H. P., or say 5,600 watts out- put, and an efficiency of say 0.8, the activity absorbed would Digitized by VjOOQ IC 292 ELECTRO-DYNAMIC MACHINERY. be 7,000 watts, or 14 amperes at 500 volts pressure. There are, approximately, 2, 100 turns in the field coils, or 700 to each pair, so that with all in series, the total M. M. F. would be 14 X 2,100 = 29,400, which might produce a flux of 2.9 megawebers through the armature. With all the coils in parallel, the M. M. F. would be three times less or 9,800, and the flux 2.12 megawebers. The ratio of speed, therefore, 2 o would be — — = 1.368, so far as regards the effect of change in magnetic flux through the armature. In practice, the speed would vary in a somewhat greater ratio, owing to the influence of greater drop in the field magnets when connected in series than when connected in parallel. We may consider, therefore, that at light loads the influence on the speed of varying the field coil connections is considerable, but at heavy loads the influence is relatively small. 371. We have seen how the speed of a motor can be con- trolled within certain limits by varying the magnetic flux use- fully passing through its armature. The same results can be effected by introducing resistance into the armature circuit. 372. If the constant torque imposed upon the motor is such as requires a current of / amperes to pass through its armature, while a given constant magnetic flux is produced by the field, and if E, be the pressure in volts across the main leads, and r, .the resistance of the armature in ohms, the drop in the armature will be Ir volts, and the armature of the motor must develop that speed which will produce a C. E. M. F. of (E — I r) volts. If it be required to reduce this speed to say, one half, then the total resistance of the armature circuit must be increased E — I r to R ohms, in such a manner that E — I R = , so ' 2 E -J- I r that R = — ^-= — . While this plan is theoretically effective, 2 / it is practically objectionable, because, in the first place, it wastes energy by the introduction of the additional resistance (R — r) ohms, the amount of activity wastefully expended in such resistance being 7 a (R — r) watts. In the second place, a comparatively small accidental variation in the torque, which Digitized by VjOOQ LC REGULATION OF MOTORS. *95 we have hitherto supposed constant, would effect a large variation in the speed, owing to the varying drop in the added resistance. Again, a powerful motor requires a powerful cur- rent strength to be supplied to it, and a large expenditure of energy is necessary in order to greatly reduce its speed in this B B, FIG. 221. — SYSTEM OF PRIME MOTOR, GENERATOR, Al»D WORKING MOTOR FOR CONTROLLING THE SPEED AND DIRECTION OF THE WORKING MOTOR. UNDER CONSTANT TORQUE. manner, requiring the use of bulky and expensive resistances, to dissipate the heat developed. For these reasons this method of maintaining the speed constant is seldom employed. 373. It has been found so difficult in practice to vary the speed of a motor at constant torque between full speed and rest, without loss of efficiency, that in cases where complete control is imperative, as in some rolling mills, where the machinery has to run occasionally at a definite very low speed, and at other times at full speed, a method, which is repre- sented in Fig. 221, has been invented and applied. Here M y is a shunt-wound motor, connected across a pair of supply mains, A A, B B, and, therefore, running at practically con- stant speed under all conditions of use. The armature of this motor is connected directly, either by a belt or by a rigid coupling, to the armature of the generator G, whose field magnets are excited through a rheostat R. The generator armature consequently runs at a practically constant speed under all conditions of service. The E. M. F., which this Digitized by VjOOQ IC 294 ELECTRO-DYNAMIC MACHINERY. generator armature develops, depends, however, upon the excitation of its field magnets, which is regulated by the rheostat R y so that, when no current passes through the generator field coils, the E. M. F. of its armature is nearly zero, while, when full current strength passes through the field coils, the E. M. F. of the generator is at its maximum. The brushes of the generator are directly connected with the brushes of the working motor m, whose field magnet is con- stantly excited, and the speed of the armature m, will be con- trolled directly by the E. M. F. of the generator G. If the generator is fully excited, the E. M. F. at the terminals of the motor m, will be a maximum, and the speed of the motor to meet this E. M. F. with a corresponding C. E. M. F. will also be a maximum, while if the generator has its excitation removed, the armature of the motor m may come almost or quite to a standstill. If necessary, the connecting wires between the armatures of G and m y can then be reversed so that the direc- tion of tn's rotation can be reversed. 374. The fact that this combination of machines operates satisfactorily without excessive sparking at the commutator of the generator, often occasions some surprise to those who are accustomed to varying the field excitation of generators and motors, under ordinary conditions, since it is known that, in general, when a generator, and particularly a motor, has its field magnets considerably weakened, a violent sparking is apt to be produced at the commutator. It is to be remembered, however, in this case, that the armature of the weakened generator G, is never permitted to send more than the full- load current strength, which is required to overcome the full- load torque, while on the contrary, if this machine were employed across constant-potential mains as a motor and the magnetic flux through the armature was considerably weakened, the current strength which would pass through the armature would be, probably, much in excess of the full-load current, with a corresponding tendency to produce excessive armature reaction and sparking. 375. Although the preceding combination of apparatus effects the desired result of varying or reversing the speed of Digitized by VjOOQ LC REGULATION OF MOTORS. 295 the motor at will, under constant or even under variable torque, within the limits of full load, yet it has the double disadvan- tage of requiring the installation of three times the amount of machinery which would otherwise be necessary, and of hav- ing a considerably reduced efficiency of operation. If, for example, the motor M % has to be a io-KW machine, then the generator G, must at least have a capacity of 10 KW, and at least an equal capacity will have to be given to the prime motor Ms so that 30 KW of machinery are installed where but 10 are directly brought into use. Again, if the commercial efficiency of each machine were 83 per cent, at full load, the commercial efficiency of the combination, under full load, would be, approximately, 0.83 X 0.83 x 0.83 = 0.572, so that the combination would have a full-load efficiency of 57.2 per cent. At light loads the combination efficiency would be still lower; for example, if at half load the efficiency of each machine were 75 per cent., the combination efficiency would be 42.2 per cent. On the other hand, however, the introduc- tion of resistance into the armature circuit of a motor, in order to reduce its speed, would probably effect as low or even a lower efficiency. It is evident, therefore, that in this direc- tion the electric motor shows its weakest side. 376. The fourth condition of working; namely, under vari- able torque and variable speed, differs from the last only in the variability of the torque. This being, as we have seen, the condition of working with street-car motors, it is probably one of the most important conditions to be met. It is met within the limits of practical requirements in street-car motors, partly by controlling the field magnets, and partly by the introduction of resistance into the armature circuits. This resistance may be added either through the series windings of ' the field coils, or by the direct insertion of external resistance. The problem, however, of qontrolling within full range the speed of a single continuous-current motor, under varying torque, with high efficiency, is, strictly speaking, yet unsolved. 377. In some cases two motors are rigidly coupled together so that they may have their armatures connected in series or in parallel. In the first case they divide the pressure of the Digitized by VjOOQ LC *9 6 ELECTRO-DYNAMIC MACHINERY. C. E. M. F. between them, so that their speed will be a mini- mum under that condition. In the second case they each take the full pressure, and so yield the maximum speed. At slow speed, however, when connected in series, it is evident that the activity of the combination will be E I watts, since each machine can now take / amperes, E 9 being the pressure be- tween the mains, in volts. At full speed, since each armature can take / amperes, the available activity will be 2 E I watts. The combined torque, for the full-load current through each armature, will be the same whether they are in parallel or ia series. Digitized by VjOOQ IC CHAPTER XXVIII. STARTING AND REVERSING OF MOTORS. 378. If a series motor be at rest, and be connected directly across the mains, then if the resistance of the armature and magnet coils together be R ohms, the current strength passing through the motor tends to become -= amperes, £ 9 being the E. M. F. in volts at the supply mains. Thus, if a i-H. P. series- wound motor has a resistance in the armature of 0.5 ohm, and a resistance in the field coil of 0.5 ohm, the total resistance in the machine will be 1 ohm, so that the first tendency is to produce a current strength of = 110 amperes, as soon as the machine is connected with the circuit, assuming the mains to have a constant pressure of no volts, whereas the full-load current strength of the machine will be about 10 amperes. As soon as the armature has become able to develop its full speed, the motor will generate such a C. E. M. F. as will limit the current through it to that required to expend the energy it wastes and delivers. The rapidity with which the armature will reach its full speed depends upon the load connected with it, upon the inertia of the armature and of its load, as well as upon the current strength entering the armature. Moreover, owing to the self induction, or inductance, of the field-magnet coils, it is impossible to develop the full current strength immediately in them, even assuming that the armature were to remain at rest. As soon as the current excites the field magnets, the flux they produce, passing through the magnetic circuit, develops in the field coils a temporary C. E. M. F., which has a powerful influence in checking the first inrush of current into the armature during the first half second or second of time. For this reason, a series-wound machine is much more safely started from rest to full speed than a shunt- wound machine, in which the' armature has to be connected directly across the mains. Digitized by VjOOQ IC 298 ELECTRO-DYNAMIC MACHINERY, 379. In all except the smallest machines of the shunt-wound type, it is necessary to insert some resistance in the armature circuit when starting from a state of rest, so that the drop produced in such resistance by the starting current may limit the amount of current passing through the armature. For this purpose special rheostats, called starting rheostats, are inserted in the armature circuit. Since they are only intended to carry the current during the time that the motor is coming up to speed, they are not usually designed to carry the full current strength of the motor indefinitely, and, therefore, a starting rheostat should never be maintained constantly in circuit. Fig. 222 represents a form of starting rheostat employed with shunt-wound motors. Here a number of coils or spirals of FIG. 222. — STARTING RHEOSTAT. galvanized iron wire, are mounted in a fire-proof frame under a cover of slate or composition, on which a number of contacts are arranged in a circle. Fig. 223 represents the manner in which such a rheostat is connected in the armature circuit. 380. If it becomes necessary, as we have shown, to insert resistance into the circuit of a shunt-wound motor armature, in order to start it from rest, it is still more necessary to insert resistance into the armature circuit, in order suddenly to reverse its direction of motion. When the armature terminals of a shunt-wound motor are suddenly reversed, relatively to the mains, while the field magnet coils remain permanently excited, Digitized by VjOOQ LC STARTING AND REVERSING OF MOTORS. 299 the E. M. F. of the armature due to its speed, which was, before the reversal, a C. £. M. F., tending to check the passage of current strength through its windings, becomes now a driv- ing £. M. F., tending to increase the current strength passing through it from the mains. The effect of a sudden reversal in a shunt-wound motor armature is, therefore, practically equiva- lent to suddenly throwing the armature across a pair of mains having double the pressure of those actually employed, and FIG. 223. — CONNECTIONS OF STARTING RHEOSTAT WITH SHUNT MOTOR. with the attending consequences of an enormous overload of current strength, which first checks, and then reverses, the direction of armature rotation. 381. Various devices are employed for preventing a motor armature from being injured by the sudden reversal of its terminals with the mains. At the time when armatures were almost all of the smooth-core type, damage was frequently done by shearing the wires off the armature core under the very heavy Digitized by VjOOQ LC 3°° ELECTRO-DYNAMIC MACHINERY, FIG. 224.-^FORM OF AUTOMATIC SWITCH. electro-magnetic stresses thus brought to bear upon them dur- ing rotation. When toothed-core armatures became generally used this danger practically disappeared, but the danger of damaging either the insulation of the wires, or the mechanical framework of the armature, or of burning out some of the con- Digitized by VjOOQ LC STARTING AND REVERSING OF MOTORS. 3°* •ductors, still remains. A starting coil is frequently employed with street-car motors which consists of a coil of strip-iron -conductor, having a hollow interior, so that it contains a large bvwwwwtl' FIG. 225. — CONNECTIONS FOR AUTOMATIC SAFETY SWITCH AND STARTING RHEOSTAT. magnetic flux when excited. The C. E. M. F. suddenly developed from such a coil, on being magnetized, is sufficiently great, to check, for the moment, the first rush of current, and such a coil may be called an inductance coil. 382. Fig. 224, represents the form, and Fig. 225, the diagram- matic connections of a particular automatic switch and starting Digitized by VjOOQ IC 302 ELECTRO-DYNAMIC MACHINERY. rheostat sometimes employed with large motors. The larger the motor the more expensive does any accident become which may happen to its armature, and the more economical it becomes to take precautions against such accidents. Referring^ to the figures, it will be s«en that the mains or line wires are connected directly to two circular contact segments S f S f through the coils of a relay magnet 11. When the handle H y is in such a position that the two contact bars 2?, 2?, rest in the intermediate position, they lie out of contact with the seg- ments, and the current is then entirely cut off the motor. A powerful spring, wound about the axis on which the handle ff 9 moves, tends to bring the handle and the bars £, 2?, back to this zero or "off" position. If the handle is pressed forward in the clockwise direction against the pressure of its spring, the line wires are connected with the armature through the resistance coils r> r, r, which are wound upon spools of insulat- ing and non-inflammable material within the box, and also through the field coils of the motor. When the handle is pushed completely around to the "on " position, the extra re- sistances are cut out of the armature circuit and the armature thus becomes enabled to run at full speed. In this positioa the handle is prevented from returning to zero and is kept in place by the detent magnet D, excited by the current passing* through the field coils. If the circuit of the field coils should accidentally become broken, the magnet D, will release its. armature, which will release the detent, which will allow the handle If, with its contact bars 2?, 2?, to return to the " off " position, under the action of the spiral spring; or, should the armature current become excessively strong, thereby endanger- ing the armature, the relay magnet will attract its armature, which will thereby short-circuit the detent magnet, and the same result will follow. The armature will, therefore, be stopped by any overload, and will be cut out of circuit by any- accidental cessation of the current in the field. By means of a push-button circuit, the armature can be brought to rest, by- pressing a push button placed at any distance from the machine. 383. All the phenomena of armature reaction which we have traced in cpiateetiwwith dynamos in Pars. 198 to 223 are pre- Digitized by VjOOQ LC STARTING AND REVERSING OF MOTORS. 3°3 sen ted by motors, with the exception that the direction of the M. M. F. of the armature, relatively to the field magnets, is reversed ; that is to say, a motor runs so that the magnetic flux produced by its armature tends to pass through the pole which the armature approaches; /. c, the leading pole, instead of the trailing pole, or that from which it is forced in the dynamo. With this exception all the effects of sparking and cross-magnetization present themselves equally in motors as in dynamos. The diameter of commutation in a generator has to be advanced in order to obtain a sparkless position; in other words, a lead has to be given to the brushes, while in a motor the diameter of commutation has to be retrograded to arrive at the same result; in other words, a lag has to be given to the brushes. 384. In order to reverse the direction of rotation of a motor, a single rule has to be borne in mind; namely, the M. M. F. either of the field or of the armature must be reversed. If the M. M. F. of both field and armature be simultaneously reversed, the direction of rotation of the motors remains unaltered. 585* Fig. 226 is a complete diagram showing the relations which exist between the direction of rotation and the direction of current in the field and armature of different machines. The horizontal row on the top represents separately-excited machines; the next lower row, shunt- wound machines, and the lowest horizontal row, series-wound machines. The. first vertical column, No. I, on the right, represents generators. Column II, next in order to the left, represents the action of these machines as motors, when mounted in connection with the mains, but not supplied with sufficient driving power to maintain the machines as generators. Column III represents the effect of reversing the connection of the armature when the machine is acting as a motor. Column IV represents the effect of reversing the field connections instead of the con- nections of the armature. Column V represents the effect of reversing both field and armature connections, which is equiv- alent to reversing the ^entire machine -relatively to the mains. The large arrow on the field coil represents the direction of Digitized by VjOOQ IC 304 ELECTRO-DYNAMIC MACHINERY. the M. M. F., or of flux through the field. The large arrow on the armature represents the direction of the M. M. F. in the armature, due to the current. The small arrow in the centre of the armature represents the direction of the arma- 8 O S o Z O % H O * fa o 01 z o z h < V H Z < < CI s ture E. M. F., relatively to the circuit, and the curved arrow, outside the armature, represents the direction of rotation of the armature. 386. Referring to the line or row of separately-excited machines, in Column I, each machine appears as a generator, Digitized by VjOOQ LC STARTING AND REVERSING OF MOTORS. 3°5 rotated by the driving belt in the direction of the curved arrow. The £. M. F. of the armature is ia the direction of the current through the armature, and the mains are supplied with current from the brushes, as shown. If the driving belt be suddenly thrown off the armature pulley, the machine will run for a few moments by its inertia, still supplying current to the mains, until the power so expended has absorbed the sur- plus energy of motion of the armature, when the speed and E. M. F. of the armature will diminish, until the E. M. F. is exactly equal to that between the mains, which are assumed to be maintained at a constant difference of potential by another source of supply. At this moment there will be no current through the armature. If there weFe no friction in the arma- ture, this condition might be retained indefinitely, but since every machine must expend energy against frictions, the speed of the armature continues to slacken, and the E. M. F. in the armature falls below that in the mains. Current will then pass back from the mains through the armature, as shown in Column II, reversing the M. M. F. of the armature, but maintaining the same direction of rotation. The machine is now rotated as a motor, absorbing energy from the mains, and the E. M. F. of the armature is now a C. E. M. F., as shown by the opposi- tion between the directions of the small arrow in the centre of the armature, and the arrows representing the direction of current through the armature. Consequently, a separately- excited machine runs in the same direction as generator or motor, if no change is made in the armature or field connec- tions. If the armature connections be reversed, as represented in Column III, or if the field connections be reversed, as rep- resented in Column IV, the direction of rotation of the arma- ture is reversed; but, if both field and armature connections be reversed, as in Column V, the original direction of rotation is retained. 387. In the shunt-wound machines, represented in the second row, practically the same conditions are observed to follow; namely, if the driving belt be thrown off the pulley of the machine acting as a generator, when connected to constant- potential mains, current will pass through the armature in the opposite direction to that which passes when the machine is a Digitized by VjOOQ IC 3©6 ELECTRO-DYNAMIC MACHINERY. generator, thus reversing the M. M. F. of the armature, but maintaining the direction of rotation. Reversing either the field or the armature, reverses the direction of rotation, but reversing the entire machine; /. t. 9 both field and armature, has no effect upon the direction of rotation. 388. The third row ; viz. , that of series-wound machines, dif- fers, however, essentially from the foregoing. Here, it will be observed, that if the belt be thrown off the generator, as soon as the E. M. F. of the armature is brought down to that existing between the mains, no current passes through the mains and the field magnets lose their excitation. It will follow from this that the.E. M. F. of the armature will very rapidly dis- appear, and a large rush of current will pass through the arma- ture from the mains, reversing the direction, not only of the armature M. M. F., but also of the field M. M. F., so that the machine is first brought to a standstill, and then rotated in the opposite direction. It is clear, therefore, from this considera- tion, why series- wooind machines are never employed as inde- pendent units, in parallel, for supplying a system of mains; for, if by any acccident the engine driving a series- wound generator failed to maintain the E. M. F. of its armature above that of the mains, the machine would become a short circuit upon the mains, and an enormous rush of current, with a correspond- ingly violent mechanical effort, would be brought to bear upon- the machine, tending to reverse its motion and drive the engine backward. 389. If the series-wound machine be considered as runnings in the direction represented in Column II, and the armature connections are then reversed, or the field magnet connections- reversed, as in Columns III and IV, the direction of rotation of the armature will be reversed, or restored to the direction of rotation as a generator ; while, if both field and armature be reversed, as shown in Column V, the direction of rotation will be the same as in Column II. 390. It is evident, therefore, from an inspection of the diagram, that it is only necessary either to reverse the direc- tion of the M. M. F. in the armature or in the field, to reverse Digitized by VjOOQ LC STARTING AND REVERSING OF AfOTORS. 3°7 the direction of rotation of the motor, and that the relative direction of the M. M. F. in field and armature is opposite in a motor to what it is in the same machine as a generator. For this reason the leading pole-pieces of a machine, when operating as a generator, and the following pole-pieces when operating as a motor are weakened by armature reaction. 391. In practice, it is always the connections of the armature of a machine which are reversed, in order suddenly to reverse the direction of its rotation, for the reason that the inductance of the armature being usually much less than that of the field, the change is more readily effected, and with less danger of injuring the machine by an excessive rise of pressure. On the other hand, if the machine be brought to rest and dis- connected from the circuit, it may be just as convenient to reverse the field magnet connections as the armature connec- tions, in order to effect a reversal of rotary direction when the machine is next started. 392. In all cases it has to be remembered that it is dangerous to break? the circuit of the field magnets of a motor when in operation, not only because by so doing the M. M. F. of the field is almost entirely removed, and thereby the armature is unable to develop a C. E. M. F., becoming practically a short circuit on the mains; but also, because the powerful E. M. F. generated in the field coils by self-induction, when their circuit is interrupted, may find a discharge through the armature insulation, in such a manner as to pierce the same and per- manently injure the armature. The same remarks apply to the operation of machines as generators. The field magnet connections should always be the first to be completed, and the last to be interrupted, when the machine is operated in either capacity. 393. In some cases, it is possible for the M. M. F. of the armature to overcome that of the field magnets, and actually to reverse the direction of magnetic flux through the mag- netic circuit of the machine. For example, if a shunt-wound machine be operating alone, and supplying a system of mains, it is possible for a very powerful current passing through the Digitized by VjOOQ LC $o& ELECTRO-DYNAMIC MACHINERY. armature to produce such an armature reaction as shall effect a large C. M. M. F. in the magnetic circuit of the machine, and so reverse the magnetic flux in the circuit. As soon as this is effected, the E. M. F. of the armature will be extinguished and the machine will cease to send a current. This effect is distinct from the tendency of shunt-wound generators to lower their E. M. F. under heavy loads, by reason of the drop in the armature, and its effect upon the excitation of the field mag- nets. It can only happen when the brushes of the machine are given a considerable lead; for, if the brushes be maintained at the neutral point midway between the poles, it will be impossible for the armature reaction to produce a dangerously large C. M. M. F. in the main magnetic circuit. Such acci- dents have, however, taken place in central stations with types of generator in which the armature reaction and lead of the brushes at full load is considerable. For this reason it is preferable to excite the field magnets of large central station generators from independent machines, when possible. 394. In motors, which are required to have their direction reversed, it is necessary that the brushes shall rest upon the commutator in such a position as shall permit of this reversal of direction without danger. Carbon brushes are employed with practically all 500-volt generators and motors, and with such machines for lower pressures as will permit of the passage of the full-load current through the carbon brushes without dangerously overheating them. Their advantage is that they wear evenly, lubricate the surface of the commutator, and are readily replaced. Their only disadvantage is their high resistivity, and the noise they are apt to make if the commuta- tor surface is not perfectly uniform. Digitized by VjOOQ IC CHAPTER XXIX. METER-MOTORS. 395. It sometimes becomes necessary to design a motor, whose speed shall be proportional to the current strength passing through it. This problem arises in devising motor- meters for determining the quantity of electricity supplied to a Customer from a pair of constant-potential mains, as in elec- tric lighting. The motors employed for this purpose are of very small sizes. We propose to consider the conditions under which the speed of the motor shall be proportional to the driving current strength. 396. Fig. 227 represents a pair of constant-potential mains, marked + and — , with a small motor Jf f designed to measure the current strength supplied to the incandescent lamps, L Z, with which it is connected in series. It is evident that the current which passes through the motor armature will vary directly with the number of lamps which are turned on. The connections of the motor field magnets are not shown. These magnets may be constantly excited from the mains, thus virtu- ally constituting a separately-excited field ; or, a permanent magnet field may be employed for this purpose. In either case the strength of the field flux may be considered as inde- pendent of the load. 397. We know that (Par. 313) if /, be the current strength passing through the armature in amperes, $, the field flux, in webers, usefully passing through the armature, and w, the number of turns on the armature, counted once completely around; the torque-per-ampere, which will be exerted about the armature shaft will be # w r = cm. -dynes per ampere. If no load except friction were imposed upon the armature,, that is to say, if it were free to run without retarding torque, 309 Digitized by VjOOQ IC 3 io ELECTRO-DYNAMIC MACHINERY. beyond a frictional torque of / cm. -dynes, due to mechanical and electric frictions, then the speed which the motor would attain, as soon as the first lamp was turned on, would be very great, assuming that the torque i r, was sufficient to start the motor; for, the friction /, would be practically constant at all speeds, and if / r, be greater than /, the accelerating force being greater than the retarding forces, will continually increase the speed of the motor until the C. E. M. F. of the armature reduces the current strength to that which is needed to exactly neutralize the retarding torque. Such a small motor, therefore, if unloaded, would tend to run at a very -o M FIG 227. — MOTOR ARMATURE IN CIRCUIT WITH INCANDESCENT LAMPS. high speed and to reduce the pressure at the terminals of the lamp. •398. It is also evident that the resistance of the armature must be sufficiently small, in order that the drop and C. B< M. F. in the armature, produced by the full-load current, shall not be greater than say one per cent, of the total pressure at the mains. Let us assume that we are able to impose a load or torque upon the motor proportional to its speed. If n> be the number of revolutions-per-second made by the motor, r, the load torque in cm. -dynes will then be r = a n, where a, is a constant quantity. Under these conditions, the speed which the motor will attain will be determined by the equality of the driving and resisting torques or / r = an +/. From which n = — revolutions per second = : — - — — . .a a a Digitized by VjOOQ IC . METER-MOTORS. 3 11 399. For example, suppose a small motor to be connected as shown in Fig. 227, in circuit with 20 incandescent lamps, each taking one half ampere from a pair of mains supplied with no volts pressure. The full-load current will be 10 amperes, and, if the resistance of the armature be o. 1 ohm, the drop of pressure in the armature at full load will be 1 volt. If the torque r, of the motor be 200 centimetre-grammes, or, approximately, 200,000 centimetre-dynes per ampere of cur- rent, also if the torque due to frictions be 75 centimetre- grammes, or, approximately, 75,000 centimetre-dynes, and the torque due to load be 120 centimetre-grammes, or, approxi- mately, 120,000 centimetre-dynes-per-revolution-per-second, then, if one lamp were turned on, the current through the armature would be 0.5 ampere. The starting torque would be 100 centimetre-grammes, the resisting torque of friction, 75 centimetre-grammes, and the motor would therefore start under a resultant torque of 25 centimetre-grammes. It would accelerate until a speed of 0.208 revolution-per-second was attained, when the resisting load torque would be 0.208 x 120 =25 centimetre-grammes. Proceeding in this way, we can determine what the speed of the motor would be with any current strength as follows: Lamps. Current amperes. Moving- Torque cm.-grammes. Resisting Friction cm.'gms. Torque Speed cm.'gms. Speed 0/ motor rv. per s. Speed Per lamp rv.per s. I 0.5 IOO 75 25 0.2I 0.2I 2 I.O 200 75 125 I.04 O.52 4 2.0 4OO 75 325 2.71 0677 6 3.0 600 75 525 4-375 O.729 8 4.0 800 75 725 6.O4 0.755 10 5.0 1,000 75 925 7.71 O.771 12 6.0 1,200 75 1,125 9375 O.781 14 7.0 I,400 75 1,325 .II.04 O.789 16 8.0 I.OOO 75 1,525 12.71 0.794 18 9.O I,800 75 1,725 14375 O.799 20 I O.O 2,000 75 1,925 16.O4 0.802 Here a = I20 ,900 r = 200,000/ = 75, 000, so that with i — 2 0, n == IO X 200,000 X 75> ooc DO 6.04. I20,0< 400. It will be observed that, after the first two lamps have been lighted, the speed of the motor is nearly pro- Digitized by VjOOQ IC 312 ELECTRO-DYNAMIC MACHINERY. portional to the number of lamps, and, therefore, the total number of revolutions of a motor armature in a given time, will be an approximate measure of the total quantity of elec- tricity supplied through the meter in coulombs, or in ampere- hours. In order that the error, introduced into the indications of the meter, by constant friction of the armature, shall be as small as possible, it is important that the constant torque-per- revolution-per-second shall be as great as possible, relatively to the friction, or that — shall be a small fraction. a 401. In practice it would be very difficult to arrange a motor of this kind, having its armature placed directly in the main circuit of the lamps, for the reason that if the brushes were sufficiently fine to permit the friction of the armature to become negligibly small, any accidental short-circuit, occurring between the lamp-leads, would probably destroy the brushes, or the armature, or both. The problem has, however, been successfully met in practice by making the armature in this case the fixed element of the motor, and the field magnet the moving element. Fig. 228 represents a well-known type of meter, in which the current to be measured passes through the stationary element of the field coils F y F y while the moving element, or armature Af 9 is permanently magnetized by a feeble current passing through a comparatively high resistance, wound on a frame at the back of the instrument and kept in circuit with the mains. The armature M, receives its current through the delicate brushes £, which rest on opposite sides of a small silver com- mutator c. No iron is employed in either the field or armature of the apparatus. The. vertical shaft of the armature M, is geared directly with a dial-recording mechanism similar to that of a gas meter. In order to apply a load torque proportioned to the speed, a disc of copper Z>, is mounted horizontally upon the vertical armature axis, so as to rotate between the poles of the three permanent magnets P, P, P> as shown. When the disc is at rest there is no retarding torque other than a small mechanical friction due to the brushes resting on the commutator and the weight of the armature in its bearings. Digitized by VjOOQ IC METER-MOTORS. 313 As soon as the disc is set in motion by the rotation of the armature, eddy currents are produced in its substance by the dynamo action of the permanent magnets upon it, and a re- tarding torque is set up between the disc and these magnets. At all ordinary speeds this torque is proportional to the rate of rotation, thus complying with the requirements of the motor as a meter. 402. The armature of the motor represented in Fig. 227 is FIG. 228. — WATTMETER. only capable of acting as a coulomb meter, or ampere-frour meter, but the apparatus shown in Fig, 228, while acting as an ampere- hour meter on constant potential mains, also operates as a watt-meter, in cases where the pressure between the mains is not constant; for, all variations in the pressure will also increase in direct proportion the useful flux 0, linked with field and armature, and so the speed of the armature will be accelerated and retarded in proportion to the pressure, as well as in proportion to the current strength. Digitized by VjOOQ IC 3M ELECTRO-DYNAMIC MACHINERY. 403. No law of retarding torque, other than a torque pro- portional to the speed, can give a rate of revolution in the armature proportional to the current strength passing through it, when the field flux # is constant. If, however, the field magnets be in series with the armature, so that $ increases with the load, it is possible for an instrument of this character to register fairly accurately, even although the load torque is not proportional to the speed. In such cases, however, the results can only be approximate, since the hysteresis in the magnetic circuit of the field will bring about a complicated relation between load and flux. 404. Another problem which sometimes arises, is to design a motor whose speed shall be proportional to the pressure in \w## FIG. 229. — MOTOR ARMATURE SHUNTED AND IN CIRCUIT WITH INCANDES- CENT LAMPS. volts at its terminals. This problem presents itself in motor- meters having an armature which, instead of being inserted directly in the lamp circuit, is shunted by a constant small resistance r. A motor- meter of this type is shown in Fig. 229. Here the danger of burning out the armature by an accidental overload is not nearly so great, since the pressure at the arma- ture terminals can never exceed that of the drop in the shunt resistance r. If /', be the total current strength in amperes passing through the lamps, and e, the dynamo power of the armature, in volts-per-revolution-per-second, the current strength passing through the armature will be -t\) r —n e i r X n e L-!£ £ amperes, = * + Digitized by VjOOQ IC METER-MOTORS. 315 where R is the resistance of the motor armature in ohms, and the driving torque will be i x r cm. -dynes. If the frictional torque /, centimetre-dynes, be assumed constant, the speed of the motor will be determined by the relation /, r = / or ( / r - n e) _ * (R + r) f * from which n = J —+ — — — - revolutions-per-second. e er v From this it will be seen that the motor will develop a speed Current Current Current CE.M.F. Speed, Revolu- 2. thro' thro* ar- in shunt Drop in Drop in of arma- revolu- tions per % lamps, mature, amperes shunt, armature, ture. tions per lamp per amperes t. amperes ('-•»)• volts. volts. volts. sec., n. second. I 0.5 0.05 o-45 0.045 0.005 0.040 06.6 0.66 3 x.o 0.05 0.95 0.095 0.005 0.090 J K 075 4 2.0 0.05 1.95 0.195 0.005 0.190 3.16 0.79 6 3.0 0.05 a.95 0.295 0.005 0.290 4.83 0.805 8 4.0 0.05 3-95 o-395 0.005 0.390 6-5 0.8x3 0.816 10 5.0 0.05 4.95 0495 0.005 0.490 8.16 20 10.0 0.05 9-95 0.995 0.005 0.990 16.5 0.825 proportional to the main current /, if the frictional torque /, be constant, and sufficiently small to make — — — — - small ' J ex i t compared with — . The following case will illustrate this result. Let R = o. 1 ohm, r = o. 1 ohm, / = 50 cm.-gms.,r = 1,000 em.-gms.-per-ampere, e = 0.06 volt per revolution per second. Then n = 1.667/ — 0.1667. The preceding table shows the results which follow for various currents up to 10 amperes, either directly from the formula or by independent reasoning. Such a motor will usually operate at a comparatively high speed at full load, since it depends upon the influence of its C. E. M. F. in reducing the current strength through the armature to that required in order just to balance the resisting torque /. 405. If, however, a load torque be imposed on the armature, proportional to the speed, represented by t x = a n y then our relation becomes t\ = r f + a n Digitized by VjOOQ IC 316 i r — tie ELECTRO-DYNAMIC MACHINERY. r = / + a n, from which n = r— 44 . * y ^ e r +a (J? + r) revolutions-per-second. If, for example, in the last case, the motor develops a re- tarding torque of 60 cm. -gms. per-revolution-per-second (a = 60 cm. -gms. or 60,000 cm. -dynes approximately), we obtain either from the formula, or by direct analysis, the following results : Current. Torque. Drop in Motor Speed. Armature. i a O . C . .2 3 «2 1 i/5 s in 6 s . rt i/> "0 > in §. E J.fi Js is 3 ui S 6 S - I/I ■5 8. SJ-3 b "o > a. If £ O 3 2" 2 C/3 Is H c •1 3 o> V 3 Q 2 W O H > >" <* 1 0.5 O.083 O.4I7 0.0417 50 33 83 O.083 0.0083 0.033 O.0413 0.55 0.55 2 1 O.125 0.875 0.0875 50 75 125 O.I25 0.0125 0.075 O.0875 1.25 0.625 4 2 O.208 1.792 0.1792 50 i5« 208 O.208 0.0208 0.158 O.179 2.633 0.658 6 3 O.292 2.708 0.2708 50 242 292 O.292 0.0292 0.242 O.271 4 -03 0.667 8 4 0-37S 3-625 0.3625 50 325 375 0.375 0.0375 0.325 O.3625 5-42 0.678 10 5 O.459 4-541 0.4541 50 S°2 459 0.459 0.0459 0.409 o-454 6.82 0.682 20 10 O.876 9.124 0.9124 50 826 876 O.876 0.0876 0.826 0.913 i*-97 0.689 406. It is, therefore, evident that a motor armature, with constant field excitation, can develop a speed closely propor- tional to the pressure at its terminals, and, therefore, serve as a motor-meter, if the retarding torque be small and constant, or, if it be partly small and constant, and partly proportional to the speed. 407. One of the most important recent applications of motors is their distributed application to machine tools in large factories. Instead of employing long lines of counter- shafting, which must necessarily be constantly driven during working hours, a separate electric motor is applied directly to each machine, so that each machine is started and stopped according to its own requirements. Moreover, the range of regulation of speed, which is obtainable from a common coun- tershaftirig, is necessarily more limited in degree than that which can be effected by the use of independent motors. Digitized by VjOOQ LC METER-MOTORS. 3*7 408. By the use of individual electric motors, not only is each tool capable of operation at its best speeds, and under com- plete control, but also the friction of long lines of counter- shafting is eliminated. The economy is greatest where the nature of the work in the machine shop is such that the average power supplied to the tools is much less than the maximum power, or the ratio of average to maximum power; i. e., the load factor is small, since the motors, when completely dis- connected from a circuit, take no power, whereas, the countershafting consumes, practically, the same amount of power friction, whether the tools be active or idle. Digitized by VjOOQ IC CHAPTER XXX. MOTQR DYNAMOS. 409. The consideration of dynamos and motors naturally leads to that of a third class of apparatus^ which partakes of the nature of each; namely, motor-dynamos, or, as they are sometimes called, dyna-motors. It is evident that if a motor be rigidly connected to a dynamo, either by a belt or by a coupling, that we obtain a means whereby electric power can be transformed through the intermediary of mechanical power. Thus, the motor may be operated from a high-tension circuit, while the dynamo .operates a low-tension circuit, 6r vice versa ; but, neglecting losses taking place in the two machines, the amount of electric energy absorbed and delivered in the re- spective circuits will be the same, the combination being utilized for the purpose of transforming the pressure and cur- rent strength. For this reason a motor-dynamo is commonly called a rotary transformer, in order to distinguish it from an ordinary alternating-current transformer, which always remains- at rest. 410. Instead of rigidly connecting together two separate machines; /. e. y two armatures in two separate fields, the plan has been adopted of placing the two armatures in a field com- mon to both; as, for example, by placing them in a common field of double length. Or, a still closer union can be effected by winding both the armature and motor coils on a common armature core, care being taken to insulate the two sets of windings from each other. Under these circumstances, since the intake of the motor winding is practically equal to the out- put of the dynamo winding, the space occupied by each wind- ing will be practically the same, so that where both are asso- ciated on a common core, half the winding space is appropriated 318 Digitized by VjOOQ LC MO TOR D YNAMOS. 3 * 9 for each. The result will be that if the motor winding or dynamo winding be such as would appertain to, say, a io-KW capacity, the armature in which the two are associated will be a machine having, approximately, the size and weight corre- sponding to a 20-KW capacity. There is, however, an econ- FIG. 23O. — STEP-UP MOTOR DYNAMO. omy in constructing one machine of double capacity, instead of two machines of single capacity, both in first cost and in efficiency. 411. Rotary transformers, like all transformers, may be either of the step-up t or step-down type. Fig. 230 represents a step- up rotary transformer of 1.5-KW capacity, transforming from 120 volts and 12.5 amperes, to 5,000 volts and 0.3 ampere. The motor winding of the armature is connected with the com- mutator on the left, while the generator winding of the arma- ture is connected with the commutator on the right. The magnet coils are excited from the low-tension mains. The two armature windings, in such cases, may be either placed ope below the other, or they may be interspersed. The left hand Digitized by VjOOQ LC 320 ELECTRO-DYNAMIC MACHINERY. brushes receive the 120- volt pressure, and the right hand brushes deliver the 5,000-volt-pressure. The function of such a machine is to test high-tension insulation under practical conditions of pressure. 412. Fig. 231 represents a step-down rotary transformer for transforming from 500 to 120 volts. In this case the smaller FIG. 231. — STEP-DOWN DYNAMO. brushes are connected to the 500-volt mains, as is also the field winding, and the lower pressure is delivered at the heavy brushes. 413. It is important to observe that in a motor dynamo of the preceding types there is no appreciable armature reaction. The reason for this is as follows: The M. M. F. of the motor armature winding is, as we know, opposite in direction of that of the generator winding; and, since these M. M. Fs. are Digitized by LiOOQ LC MO TOR D YNAMOS. $2 1 nearly equal, and are produced on the same core, they will nearly neutralize each other. Consequently, the brushes of such a machine never require to be shifted during variations of load, and the commutators are characterized by quiet and sparkless operation. 414. Under ordinary circumstances it is necessary to excite the field magnet of a motor dynamo from the primary circuit, since, otherwise, the motor side could not be operated. It is often possible, however, to place a series winding on the motor side, and a shunt winding on the secondary or dynamo side. Thus, if it be required to transform from 1,000 to 50 volts, a shunt-field winding for 1,000 volts would be more expensive than one for 50 volts. In such a case it becomes possible to excite the fields by a few turns of series winding, carefully in- sulated, in the primary circuit, in order to start the machine from rest, and to supply the balance of the field excitation by a shunt winding on the secondary side, which commences to be actuated as soon as the motor starts. 415. It will be evident that any variation in the strength of the field magnets, whether these be shunt- or series-wound, will not vary the ratio of transformation; for, although by varying the field excitation the motor can be made to change speed, yet this speed will not produce any appreciable effect upon the generated E. M. F., since the field is proportionally weakened. In other words, the C. E. M. F. in the motor being always equal to the E. M. F. at the brushes, after deducting the drop in the armature, the generated E. M. R, which is always some fixed fraction of the motor C. E. M. F., must be constant within the same limits. If the number of turns in the motor winding, counted once all round the armature, be w m , and the number of turns in the generator winding, counted in the same iv manner, be 7V £ , then the ratio — - is called the ratio of transfor- mation. If, then, the primary E. M. F. be E x volts, the primary current I x amperes, and the resistance in the primary winding r x ohms, while the corresponding quantities in the secondary circuit are E^ 7 9 , and r a , respectively, the C. E. M. F. in the primary winding will be n e y = E\ — I x r t , where n, is the speed Digitized by VjOOQ IC 5-2 ELECTRO-DYNAMIC MACHINERY. of revolution in turns-per-second, and e } , the dynamo power, or w m x io~ 8 . The generated secondary E. M. F. will be n $w e X io- 8 volts = (E x — I x r x ) ^. W m The pressure at the secondary terminals will be further re- duced by the drop in the secondary winding; or * = <*.-/.'.>£-/.', If the weight of copper in the two windings is equal, 7 9 r- t , will practically be equal to —± — l — -, so that w m The machine, therefore, acts as though it were a dynamo of E. M. F. ,-L. E t> with an internal resistance of 2r, or twice that w m of the secondary winding. 416. In all motor dynamos, having a field magnet common to both armatures, the ratio of transformation, neglecting ar- mature drop, is constant, no matter how the field excitation is varied. Motor-generators are often employed for raising or lowering the pressure of continuous-current circuits. Thus electroplating E. M. Fs. of, say 6 volts, are obtainable in this manner from circuits of no, 220 or 500 volts pressure. Simi- larly, pressure of 150 volts are obtainable from a few storage batteries by such apparatus. 417. In central stations for low-pressure distribution, say at 220 volts, by a three-wire system, some of the feeders have to be maintained at a higher pressure than others, in order that all the feeding points, or points of connection between feeders and the mains, should have the same pressure. This is ac- complished either by employing separate dynamos, operated at slightly different pressures, or by introducing at the central station motor-dynamos having fheir dynamos in circuit with the feeders. Such motor-dynamos are frequently called boosters. The motor-dynamo for this purpose requires that means should be provided for regulating the E. M. F. which is to be added to the feeder circuit. This can only be done by employing separate field magnets for the motor and generator armatures. Digitized by VjOOQ IC MOTOR DYNAMOS. 3 2 3 Fig. 232 represents a practical form of booster employed in a three-wire central station. The middle machine is a motor operated at central-station pressure of, perhaps, 250 volts; the others are generators, having their armatures coupled to the same shaft as that of the motor armature. One dynamo is FIG. 232. — BOOSTER IN THREE-WIRE CENTRAL STATION. connected in circuit with the positive conductor of the feeder whose pressure is to be raised, and the other is connected in the circuit of the negative conductor. Since these feeders carry heavy currents and require to be of very low resistance, the necessity for the massive copper brushes and connections of the dynamos will be evident. The amount of E. M. F. which will be generated in these armatures will be determined by the excitation of their field magnets. THE END. Digitized by VjOOQ IC Digitized by VjOOQ LC INDEX. Active Conductor, Magnetic Flux of, 37 Aero-Ferric Magnetic Circuits, 68-73 Air-Gap, Magnetic, 57 Air-Path, Alternative Magnetic, 42 — Aligned M. M. F., 56 Alternating-Current Dynamos, 17 Alternative Magnetic Air-Path, 52 Alternators, 17 — Multiphase, 25 — Uniphase, 26 Ampere, Definition of, 49 Ampere-Hour Meter, 313 Ampere-Turn, Definition of, 40 Anomalous Magnet, 47 Arc-Light Dynamos, 26 Armature, Back Magnetization of, 186 — Cores, Cross-Sections of, 126 — , Core Discs for, 152 — Core, Lamination of, 105 — , Cylinder or Drum, 23 — Disc, 23 — , Double Winding of, 190 — , Gramme-Ring, 23 — , P R, Loss in, 200 — , Iron-Clad, Definition of, 24 — , Journal Bearings, 159-163 — of Machine, 9 — , Neutral Line of, 184 — , Pole, 110-116 — , Radial, no — Reaction and Sparking at Com- mutators, 179-198 — Ring, 23 — , Smooth-Core, 23, 152 Definition of, 24 — Toothed-Core, 152 , Definition of, 24 .23 — Turns, Effect of, on E. M. F., 3 — Winding, Closed-Coil, no , Disc, 230 , Dissymmetry of, 125 , Inter-Connected, 145 Space, 275 — Wire, Effective Length of, 246 Armatures, Closed-Coil, 217 — , Gramme-Ring, 117-127 — , Lap Winding for, 155 — , Open-Coil, 217 — , Wave- Winding for, 155 Attractions and Repulsions, Laws of Magnetic, 33 Automatic Regulation of Dyna- mos, 218 Average Efficiency of Motor, 279 Back Magnetization of Armature, 186 Balancing Coil of Armature, 194 Bar, Equalizing, 224 Bars, Bus, 224 — , Omnibus, 224 Bearings, Self -Oiling, 161 Belt- Driven Dynamos, 18, 135 Bipolar Dynamo, 16 Boosters, 322, 323 Box, Field-Regulating, for Dy- namo, 14 Brush, Dynamo, 124 Brushes, Forward Lead of, 217 — , Lead of, 185 — of Dynamo, 9 — of Motor, Lag of, 303 Bus Bars, 224 Calculation of Gramme-Ring Dy- namo Windings, 128-134 Capability, Electric, of Dynamo, 126 — , Electric, of Dynamo-Electric Machine, 4 Car Motor, 277 Characteristic Curve of Dynamos, 210 — External, of Series- Wound Dy- namo, 210 — Internal, of Series- Wound Dy- namo, 210 — of Shunt- Wound Dynamo, 212 Circuit, Magnetic, 48 — Return, for Track Feeders, 226 Circuits, Ferric-Magnetic, 55-67 — , Magnetic, Non-Ferric, 48-54 Digitized by VjOOQ LC 3*6 INDEX. Circuit, Transmission, Definition of, I Circular Distribution of Magnetic Flux Around Conductor, 37 — , Magnetic Flux, Assumed Di- rection of, 39 Closed Circular Solenoid, 50 — Coil Armature Winding, no Armatures, 217 Coefficient, Hysteretic, 174 Coil, Balancing, of Armature, 194 — , Inductance, 301 — , — of, 181 — , Starting, 301 Combinations of Dynamos in Se- ries or in Parallel , 220-227 Commercial Efficiency of Dyna- mo, 5 of Dynamos, Circumstances Affecting, 7 of Motor, 268 Commutation, Definition of, 180 — , Diameter of, 180 — , Quiet, Circumstances Favor- ing, 187 — , Sparkless, Circumstances Fa- voring, 186 Commutator, Circumstances Fa- voring Sparking at, 186 — , Forms of, 123 — of Dynamo, 9 Commutatorless, Continuous-Cur- rent Dynamo, Disc Type of, 236 Dynamos, 234 Generators, 234-240 Commutators, Sparking at, 170- 198 Compound Magnets, 105 — Winding of Dynamos, 208 Compound- Wound Dynamos, 14 , Uses for, 2ogr Conductor, Active, Magnetic Flux of, 37 Consequent Poles of Dynamo, 22 Constant-Current Dynamos, 10 Constant-Potential Dynamos, 10 Constants, Reluctivity, Table of, 65 Continuous-Current Commutator- less Dynamos, 28, 234 , Cylinder Type of, 236 Dynamo, 20 Generators, 234-240 Generator, Limitations to Output of, 203 Convention as to Direction of Cir- cular Magnetic Flux, 39 Converging Magnetic Flux, 35 Core Discs for Armatures, 152 Core, Effect of Lamination on Eddy Currents, 166 Coulomb Meter, 313 Counter Electro-Dynamic Force, 256 Cross Magnetization, 183 Currents, Eddy, 164-171 — , Eddy, Definition of, 164 — , — , Effect of Lamination of Core on, 166 — , — , Origin of, 165 Curves, Characteristic of Dyna- mos, 210 — of Reluctivity in Relation to Flux Density, 66 Cutting Process vs. Enclosing of Magnetic Flux, 82 Cycles of Magnetization, 174 Cylinder or Drum Armature, 23 — Type of Commutatorless Con- tinuous-Current Dynamos, 236 Decipolar Dynamos, 17 Density, Flux, 34 — , Prime Flux, 54 Devices, Receptive, Definition of, 1 Diameter of Commutation, 180 Diffusion, Magnetic, 52, 53 Diphase Dynamo, 27 Direct-Driven Dynamos, 135 Disc Armature, 23 — Armature Winding, 230 — Armatures and Single Field- coil Machines, 228-233 — , Faraday's, 234 — Type of Commutatorless Con- tinuous-Current Dynamos, 236 Dissymmetry, Magnetic, 124 — of Armature Winding, 125 Distribution of Magnetic Field, 41 -47 — of Magnetic Flux, 31 — of Magnetic Flux of Conductor, 37 Diverging Magnetic Flux, 35 Double Circuit, Bipolar Dynamo, 16 Double Winding of Armature, 190 Drum Armatures, 152 — or Cylinder Armatures, 23 Dynamo Armatures, Electro-Dy- namic Induction in, 90-102 — , Bipolar, 16 — Brush, 124 — Brushes of, 9 — , Commercial Efficiency of, 5 — Commutator, 9 — , Consequent Poles of, 22 Digitized by VjOOQ LC INDEX. 3*7 Dynamo, Continuous-Current, 20 — , Diphase, 27 — , Double-Circuit, Bipolar, 16 — , Electric Capability of, 126 — , — Efficiency of, 5 Dynamo-Electric Generator, 2 Machine, Electric Capability of, 5 Dynamo Field-Regulating Box, 14 — , Intake, 5 — , Load of, 15 — , Magneto-Electric, 11 — , Output of, 5 — , Plating, 26 Dynamo-Power of Motor, 266 Dynamo Relation between Output and Resistance, 6 — , Self-Excited, 12 — , — , Compound- Wound, 13 — , Separately Excited, 12 — , Single-Circuit, Bipolar, 16 — , Telegraphic, 26 Dynamos, Alternating-Current, 17 — , Arc-Light, 26 — , Automatic Regulation of, 218 — , Belt-Driven, 18 — . Characteristic Curves of, 210 — , Circumstances Influencing Electric and Commercial Effi- ciency of, 7 — , Combination of, in Series or Parallel, 220-227 — , Commutatorless Continuous- Current, 28, 234 — , Compound- Wound, 14 — , — , Uses for, 209 — , Constant-Current, 10 — , Constant-Potential, 10 — , Decipolar, 17 — , Direct-Driven, 135 — , Heating of, 199-205 — , Incandescent Light, 26 — , Inductor, 25 — , Multipolar, 16 — , Multipolar, Gramme-Ring, 135 -151 — , Octopolar, 17 — , Over-Compounded, 209 — , Quadripolar, 17 — , Regulation of, 206-219 — , Sett-Excited, Series-Wound, 13 — , Series- Wound, Uses for, 209 — , Sextipolar, 17 — , Shunt-Wound, Uses for, 209 — , Simple Magnetic Circuits, 22 — , Single-Field-Coil, Multipolar, 28 — , Single-Phase, 27 — , Three-Phase, 27 Dynamos, Triphase, 27 — , Two-Phase, 27 — , Unipolar, 28 Dynamo tors, 317 Dyne, Definition of/ 69 E. M. P., Effect of Number of Armature Turns on, 3 — , Effect of Speed of Revolution on, 3 — , Induced by Magneto Genera- tors, 103-109 — , Induced in Loop, Rule for Direction of, 94 — , of Electro-Dynamic Induction, Value of , 75-82 — , of Self-induction, 181 — , of Self -Induction, Circum- stances Affecting Value of, 182 — , Produced by Cutting Earth's Flux, 90 Earth's Flux, E. M. F. Produced by Cutting, 90 Eddy Currents, 164-171 , Definition of, 164 , Effect of Lamination of Core on, 166 , Formation of, in Pole-pieces, 169 , Origin of, 165 Edges, Leading, of Pole-pieces, 184 Efficiency, Average, of Motor, 270 — , Full Load of Motor, 270 — of Motors, 268-279 Electric Capability of Dynamo, 126 — — of Dynamo-Electric. Ma- chine, 5 — Efficiency of Dynamos, Circum- stances AJffecting, 7 — Flux, Unit of, 49 Electro-Dynamic Force, 241-249 — Induction, 75-82 in Dynamo Armature, 90-102 , Laws of, 74-89 — Machinery, 1 — Machinery, Classification of, 1 Enameled Rheostats, 216 Entrefer, 105 Equalizing Bar, 224 Ether, Assumed Properties of, 29 Ether Path of Reluctivity, 60 External Characteristic of Series- Wound Dynamo, 210 Factor, Leakage, 132 — , Load, 317 Faraday's Disc, 234 » Feeders for Return Track, 226 Digitized by VjOOQ IC 3*8 INDEX. Eeedin ; Points, 322 Ferric Magnetic Circuits, 55-67 ' — Path of Metallic Reluctivity, 60 Field Magnet of Machine, 9 — , Magnetic, 32 — Magnets, P R Losses in, 199 — Poles, Eddy-Current Losses in, 200 — Regulating Box for Dynamo, 14 — Rheostats, 215 Fleming's Hand Rule for Dyna- mos, 74 Motors, 243 Flux, Circular Magnetic, Conven- tion as to Direction of, 39 — , Converging Magnetic, 35 — Density, 34 — , Diverging Magnetic, 35 — , Magnetic, Unit of, 49 — Density, Prime, 54 — , Prime, 56 — , Magnetic, 29 — , — , Distribution of, 31 — , — , Irregular, 35 — , — , Variations of, 33 — Paths, Magnetic, 2 Following Edges of Pole-Pieces, 184 Force, M. M., Induced, 56 — , Electro-Dynamic, 241-249 — , Lines of Magnetic, 34 — , Magnetic, Tubes, 35 — , Magnetizing, 53 — , Magnetomotive, 31 — , — , Prime, 56 Forces, Electromotive, Methods for Increasing, 3 French Measures, Table of, 8 Friction Losses in Bearings and Brushes, 201 — , Magnetic, 174 Full-Load Efficiency of Motor, 270 Gap, Magnetic Air, 57 Gauss, Definition of, 35 Generator Armature, Limiting Temperature of, 203 — , Dynamo-Electric, 2 Generators, Commutatorless Con- tin uous-Current, -234-240 — , Definition of, 1 Gilbert, Definition of, 40 Gramme-Ring Armature, 23 — Armatures, 1 17-127 — Dynamos, Multipolar, 1 35-1 51 Hand Rule, Fleming's, for Dyna- mos, 74 Heating of Dynamos, 199-205 Hysteretic Activity, Table of, 175 — Losses in Armature and Field Poles, 200 — Loss, 174 — Coefficient, 174 Hysteresis, Magnetic, 172-178 — , — , Definition of, 172 Incandescent Light Dynamos, 26 Individual Electric Motors, 317 Idle Wire on Armature, 100 Inductance Coil, 301 — of Coil, 181 Induction, Electro-Dynamic, 75-82 — , — , Laws of, 74-89 — in Dynamo Armature, 90-102 — , Self, E. M. F. of, 181 Inductor Dynamos, 25 Intake of Dynamo, Definition of, 5 Inter-Connected Armature Wind- ing, 145 Internal Characteristics of Series- Wound Dynamo, 210 Iron-Clad Armature, 24 Irregular Magnetic Flux, 35 Joint Reluctivity, 60 ournal Bearings for Armatures,. 159-163 Lag of Motor Brushes, 303 Lamination of Armature Core, 105 Lamp, Pilot, Definition of, 12 Lap Winding for Armatures, 155 Laws of Electro-Dynamic Induc- tion, 74-89 Magnetic Attractions and Repulsions, 33 Lead, Forward, of Dynamo Brushes, 217 — of Brushes, 195 Leading Edges of Pole-pieces, 184 — Pole of Motor, 303 Leakage Factor, 132 — , Magnetic, 52, 53 Length, Effective, of Armature Wire, 246 Limitation to Output of Continu- ous-Current Generator, 203 Limiting Temperature of Genera- tor Armature, 203 Line, Neutral, of Armature, 194 Lines of Magnetic Force, 34 — , Stream, 30 Load Factor, 317 — of Dynamo, 15 Locomotors, 273 Digitized by VjOOQ IC INDEX. 3*9 Loss by Eddy Currents in Arma- ture and Field Poles, 200 — , Hysteretic, 174 — , — , in Armature and Field Poles, 200 Losses, I* R, in Field Magnets, 199 — in Armature, I' R, 200 — Produced by Air-Churning, 201 Friction in Bearings and Brushes, 201 M. M. F., Aligned, 56 — , Induced, 56 — , Methods of Producing, 38 — , Prime, 56 — , Structural, 56 — , Unit of, 40 Machine, Armature of, 9 — Circumstances Influencing Electric Efficiency of Dyna- mos, 7 — , Field Magnet of, 9 — , Magnetic Flux Produced by, 9 Machinery, Electro-Dynamic, 1 — , — , Classification 01, 1 Machines, Disc Armature and Single Field-Coil, 228-233 Magnet, Anomalous, 47 — , Mechanical Analogue of, 30 — , North-Seeking Pole of, 29 Magnets, Compound, 105 — .Molecular, 56 Magnetic Air-Gap, 57 — Air Path, Alternative, 52 — Attractions and Repulsions, Laws of, 33 — Circuit, 48 — Circuit, Application of Ohm's Law to, 49 — Circuits, Aero-Ferric, 68-73 — Diffusion, 52, 53 — Field, 32 — Dissymmetry, 124 — Field, Distribution of, 41-47 , Method of Mapping, 32 , Negatives of, 32 — — , Photographic Positives of, 32 — Flux, 29 , Converging, 35 , Cutting Process, Enclos- ing, 82 Density, 34 , Diverging, 35 , Effect of, on C. E. M. F., 58 , Irregular, 35 of Dynamo, 9 , Uniform, 35 , Unit of, 49 , Unit of Intensity of, 35 Magnetic Flux, Variations of, 33 — Force, Tubes of, 35 — Friction, 174 — Hysteresis, 172-178 , Definition of, 172 — Intensity, 34 — Leakage, 52, 53 — Permeability, 55 , Definition of, 3 — Potential, Fall of, 53 — Reluctance, 48 Magnetism, Definition of, 29 — , Molecular, 56 — , Residual, 55, 173 — , Streaming-Ether Theory of, 29 Magnetization, Back, of Arma- ture, 186 — , Cross, 183 — , Cycles of, 174 Magnetizing Force, 53 in Relation to Reluctivity, 59 Magneto-Electric Dynamo, 11 Magneto Generators, E. M. F. Induced by, 103-109 Magnetomotive Force, 31 Mapping of Magnetic Field, 32 Mecnamcal Analogue of Mag- net, 30 Meter Motors, 309-317 Methods for Suppressing Spark- ing, 189 Molecular Magnetism, 56 — Magnets, 56 Motor, Average Efficiency of, 270 — , Commercial Efficiency of, 268 — , Dynamo-Power Of, 264 — Dynamos, 318-323 — , Definition of, 318 — , Full-Load Efficiency of, 270 — , Leading Pole of, 303 — Torque, 251-267 — , Trailing Pole of, 303 Motors, Efficiency of, 268-279 — , Fleming's Hand Rule for, 243 — for Street Car, 277 — , Individual Electric, 217 — , Regulation of, 280-296 — , Slow Speed, 271 — , Starting and Reversing of, 291 -308 — , Stationary, 273 — , Traveling, 273 Multiphase Alternators, 26 Multipolar Dynamos, 16 , Single-Field-Coil, 28 — Gramme-Ring Dynamos, 135- 151 Digitized by VjOOQ IC 33° •INDEX, Negatives of Magnetic Fields, 32 Neutral Line of Armature, 184 — Wire of Three-Wire System, 221 Non-Ferric Magnetic Circuits, 48-54 North-Seeking Pole of Magnet, 29 Octopolar Dynamos, 17 Oersted, Definition of, 49 Ohm, Definition of, 49 Ohm's Law, 49 Applied to Magnetic Cir- cuit, 49 Oilers, Sight-Feeding, 160 Omnibus Bars, 224 Open-Coil Armatures, 217 Over-Compounded Dynamos, 209 Output and Dimensions of Dyna- mos, Relation Between, 136 — of Dynamo, Definition of, 5 , Relation Between and Re- sistance, 6 Permeability, Magnetic, 55 — , — , Definition of, 3 Photographic Positives of Mag- netic Fields, 32 Pilot Lamp, Definition of, 12 Plating Dynamo, 26 Points, Feeding, 322 Pole Armature, 25 -~ Armatures, 110-116 — , Leading, of Motor, 303 — , North-Seeking of Magnet, 29 — , South-Seeking, 29 — , Trailing, of Motor, 303 Pole-Pieces, Following Edges of, 184 — , Formation of Eddy Currents in, 169 — , Leading Edges of, 184 Poles, Consequent, of Dynamo, 22 Potential, Magnetic, Fall of, 53 Prime Flux, 56 — Flux Density, 54 — M.M. F.,56 Properties, Assumed, of Ether, 29 euadripolar Dynamos, 17 uiet Commutation, Circumstan- ces Favoring, 187 Radial Armature, no Ratio of Transformation, 321 Receptive Devices, Definition of, 1 Regulation of Dynamos, 206-219 — of Motors, 280-296 Reluctance, 48 — , Magnetic, 48 Reluctance, Unit of, 49 Reluctivity, 48 — , Constants, Table of, 65 — Curves in Relation to Flux Density, 66 — , Ether Path of, 60 — in Relation to Magnetizing Force, 59 — , Joint, 60 — , Metallic, Ferric Path of, 60 Residual Magnetism, 55, 173 Resistivity, 48 Return Track Feeders, 226 Reversing and Starting of Motors* 291-308 Rheostats, Enameled, 216 — , Field, 215 — , Starting, 298 Ring Armature, 23 Ring Armatures, Gramme, 117- 127 Rotary Transformers, 318 Rule, Fleming Hand, for Motors,. 243 — for Direction of E. M. F. In- duced in Loop, 94 Self-Excited Compound-Wound Dynamo, 13 — Dynamo, 12 — Series- Wound Dynamos, 13 Self-induction, E. M. F., of, 181 — E. M. F., of, Circumstances Af- fecting Value of, 182 Self-Oiling Bearings, 161 Separately-Excited Dynamo, 12 Series or Parallel Combinations of Dynamos, 220-227. — Winding of Dynamos, 206 Series-Wound Dynamo, External Characteristic of, 210 — Dynamo, Internal Character- istic of, 210 Sextipolar Dynamo, 17 Shunt Winding of Dynamos, 207 Shunt- Wound Dynamo, Charac- teristic of, 212 — Dynamos, Uses for, 209 Sight-Feeding Oilers, 160 Simple Magnetic Circuit Dyna- mos, 22 Single-Circuit Bipolar Dynamo, 16 Single Field-Coil Multipolar Dy- namos, 28 Single-Phase Dynamos, 27 Slow Speed Motor, 271 Smooth-Core Armature, 23 — Armatures, 152 Digitized by VjOOQ IC INDEX. 33* Smooth-core Armature, Definition of, 24 Solenoid, Closed Circular, 50 Sources, Electromotive, 2 South-Seeking Pole, 29 Space for Armature Winding, 275 Sparking and Armature Reaction, 179-198 — at Commutator, Circumstances Favoring, 186 — , Definition of, 180 — , Methods for Suppressing, 189 Sparkless Commutation, Circum- stances Favoring, 186 Specific Resistance, 48 Speed of Revolution, Effect of, on E.M.F.,3 Starting and Reversing of Motors, 291-308 — Coil, 301 — Rheostats, 298 Stationary Motors, 273 Step-Down Transformers, 319 Step-Up Transformers, 319 Stream Lines, 30 Streaming-Ether Theory of Mag- netism, 29 Structural M. M. F., 56 System, Three- Wire, 221 Table of French Measures, 8 — of Hysteretic Activity, 175 — of Reluctivity Constants, 65 Telegraphic Dynamo, 26 Thermal Losses, 204 Three-Phase Dynamos, 27 Three Phasers, 27 Three-Wire System, 221 , Neutral Wire of, 221 Toothed-Core Armature, 23 , Definition of, 24 — Armatures, 152 Torque, Definition of, 251 — , Motor, 251-267 Transformation, Ratio of, 321 Transformers, Rotary, 318 — , Step-Down, 319 — , Step-Up, 319 Transmission Circuits, Definition of, 1 Travelling Motors, 273 Triphase Dynamos, 27 Triphasers, 27 Tubes of Magnetic Force, 35 Turns, Armature, Effect of, on E. M. F., 3 Two-Phase Dynamos, 27 Two Phasers, 27 Uniform Magnetic Flux, 35 Uniphase Alternators, 26 Unipolar Dynamos, 28, 234 Unit of Electric Flux, 49 Force, in C. G. S. System, 68 M. M. F.,40 Magnetic Flux, 49 Intensity, 35 Reluctance, 49 Variations of Magnetic Flux, 33 Volt, Definition of, 49 Voltaic Analogue of Aero-Ferric Circuit, 69 Simple Ferric Circuit, 69 — Circuit, Magnetic Analogue of, 53 Wattmeter, 313 Wave Winding for Armatures, 155 Weber, Definition of, 49 Winding, Closed-Coil Armature, no — , Compound, of Dynamos, 208 — , Disc Armature, 230 — for Armature, Inter-Connected, 145 Armatures, Lap, 155 Armature, Wave, 155 — of Gramme-Ring Dynamo, Cal- culations of, 128-134 — , Shunt, of Dynamos, 207 — , Space, for Armature, 275 Wire, Armature, Effective Length of, 246 — , Idle, on Armature, 100 — , Neutral, of Three-wire System, 221 Digitized by VjOOQ IC Digitized by VjOOQ IC Digitized by VjOOQ IC Digitized by VjOOQ IC Digitized by VjOOQ IC MM MQOK18 IBTO W RETURN TO the circulation desk of any University of California Library or to the NORTHERN REGIONAL LIBRARY FACILITY Bldg, 400, Richmond Field Station University of California Richmond, CA 94804-4698 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS 2- month loans may be renewed by calling (415) 642-6753 Vyear loans may be recharged by bringing books to NRLF Renewals and recharges may be made 4 days prior to due date DUE AS STAMPED BELOW JUN 41992 Digitized by Gc YC 69677 7-7 6503Z THE UNIVERSITY OF CALIFORNIA LIBRARY 1 sw if Digitized by VjOOQ IC